3
3.0
Jun 28, 2018
06/18
by
Mozhgan Entekhabi; Kirk E. Lancaster
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Consider a solution $f\in C^{2}(\Omega)$ of a prescribed mean curvature equation \[ {\rm div}\left(\frac{\nabla f}{\sqrt{1+|\nabla f|^{2}}}\right)=2H(x,f) \ \ \ \ {\rm in} \ \ \Omega, \] where $\Omega\subset \Real^{2}$ is a domain whose boundary has a corner at ${\cal O}=(0,0)\in\partial\Omega.$ If $\sup_{x\in\Omega} |f(x)|$ and $\sup_{x\in\Omega} |H(x,f(x))|$ are both finite and $\Omega$ has a reentrant corner at ${\cal O},$ then the radial limits of $f$ at ${\cal O},$ \[ Rf(\theta) \myeq...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1510.05288
4
4.0
Jun 28, 2018
06/18
by
Beomjun Choi; Ki-Ahm Lee
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In this paper, we investigate generalized Carleman kinetic equation for n$\ge$2 and prove convergence towards the solution of equation with fast diffusion or porous medium type, $u_t=\Delta u^m$ ($0\le m\le2$), in its diffusive hydrodynamic limit. Using comparison principle of system combined with fixed speed propagation property of transport equation, we create a new barrier argument for this hyperbolic system. It is crucial to construct explicit local sub and solution of system and this is...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1510.08997
4
4.0
Jun 28, 2018
06/18
by
Giovany M. Figueiredo; Jefferson A. Santos
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We show the existence of a nodal solution with two nodal domains for a generalized Kirchhoff equation of the type $$ -M\left(\displaystyle\int_\Omega \Phi(|\nabla u|)dx\right)\Delta_\Phi u = f(u) \ \ \mbox{in} \ \ \Omega, \ \ u=0 \ \ \mbox{on} \ \ \partial\Omega, $$ where $\Omega$ is a bounded domain in $\mathbf{R}^N$, $M$ is a general $C^{1}$ class function, $f$ is a superlinear $C^{1}$ class function with subcritical growth, $\Phi$ is defined for $t\in \mathbf{R}$ by setting $...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1511.04980
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9.0
Jun 28, 2018
06/18
by
Benjamin Melinand
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This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We prove a local wellposedness theorem for the water waves equations with vorticity and Coriolis force, taking into account the dependence on various physical parameters and we justify rigorously the shallow water model. We also consider a possible non constant...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1511.07407
4
4.0
Jun 28, 2018
06/18
by
Qiaoling Chen; Fengquan Li; Feng Wang
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In this paper, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward or downward along the resource gradient. We show that the dynamics of this model can be classified into four cases, which forms a spreading-vanishing quartering. The notion of the minimal habitat size for spreading is introduced to determine if species can always...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1511.07994
4
4.0
Jun 28, 2018
06/18
by
A. Aghajani
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We consider the fourth order problem $\Delta^{2}u=\lambda f(u)$ on a general bounded domain $\Omega$ in $R^{n}$ with the Navier boundary condition $u=\Delta u=0$ on $\partial \Omega$. Here, $\lambda$ is a positive parameter and $ f:[0,a_{f}) \rightarrow \Bbb{R}_{+} $ $ (0 < a_{f} \leqslant \infty)$ is a smooth, increasing, convex nonlinearity such that $ f(0) > 0 $ and which blows up at $ a_{f} $. Let $$0
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1512.01526
5
5.0
Jun 29, 2018
06/18
by
Anna Kostianko; Edriss Titi; Sergey Zelik
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The effect of rapid oscillations, related to large dispersion terms, on the dynamics of dissipative evolution equations is studied for the model examples of the 1D complex Ginzburg-Landau and the Kuramoto-Sivashinsky equations. Three different scenarios of this effect are demonstrated. According to the first scenario, the dissipation mechanism is not affected and the diameter of the global attractor remains uniformly bounded with respect to the very large dispersion coefficient. However, the...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1601.00317
3
3.0
Jun 29, 2018
06/18
by
Tuhina Mukherjee; K. Sreenadh
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In this article, we study the following fractional Laplacian equation with critical growth and singular nonlinearity $$\quad (-\Delta)^s u = \lambda a(x) u^{-q} + u^{2^*_s-1}, \quad u>0 \; \text{in}\; \Omega,\quad u = 0 \; \mbox{in}\; \mathbb{R}^n \setminus\Omega,$$ where $\Omega$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary $\partial \Omega$, $n > 2s,\; s \in (0,1),\; \lambda >0,\; 0 < q \leq 1 $, $\theta \leq a(x) \in L^\infty(\Omega)$, for some $\theta>0$ and...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1602.07886
3
3.0
Jun 30, 2018
06/18
by
Keith Promislow; Qiliang Wu
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The functionalized Cahn-Hilliard (FCH) equation supports planar and circular bilayer interfaces as equilibria which may lose their stability through the pearling bifurcation: a periodic, high-frequency, in-plane modulation of the bilayer thickness. In two spatial dimensions we employ spatial dynamics and a center manifold reduction to reduce the FCH equation to an 8th order ODE system. A normal form analysis and a fixed-point-theorem argument show that the reduced system admits a degenerate 1:1...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1410.0447
4
4.0
Jun 30, 2018
06/18
by
Viorel Barbu
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THis work is a survey of a few nonlinear PDE based models in image restoring.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1410.3591
4
4.0
Jun 30, 2018
06/18
by
Dorian Goldman
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We study a non-local Cahn-Hilliard energy arising in the study of di-block copolymer melts, often referred to as the Ohta-Kawasaki energy in that context. In this model, two phases appear, which interact via a Coulombic energy. As in our previous work, we focus on the regime where one of the phases has a very small volume fraction, thus creating "droplets" of the minority phase in a "sea" of the majority phase. In this paper, we address the asymptotic behavior of...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1410.7047
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20
Jun 30, 2018
06/18
by
Piotr Biler; Tomasz Cieślak; Grzegorz Karch; Jacek Zienkiewicz
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We consider two-dimensional versions of the Keller--Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solutions in terms of suitable Morrey spaces norms are derived. Moreover, the impact of the consumption term on the global-in-time existence of solutions is analyzed for the classical Keller--Segel system.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1410.7807
3
3.0
Jun 30, 2018
06/18
by
F. Ali Mehmeti; F. Dewez
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In this paper, we improve slightly Erd\'elyi's version of the stationary phase method by replacing the employed smooth cut-off function by a characteristic function, leading to more precise remainder estimates. We exploit this refinement to study the time-asymptotic behaviour of the solution of the free Schr\"odinger equation on the line, where the Fourier transform of the initial data is compactly supported and has a singularity. We obtain uniform estimates of the solution in space-time...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1412.5792
4
4.0
Jun 30, 2018
06/18
by
Masaaki Uesaka; Masahiro Yamamoto
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We consider a time-dependent structured population model equation and establish a Carleman estimate. We apply the Carleman estimate to prove the unique continuation which means that Cauchy data on any lateral boundary determine the solution uniquely.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1412.7402
5
5.0
Jun 30, 2018
06/18
by
Yuanze Wu; Tsung-fang Wu; Wenming Zou
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In this paper, we study the following two-component systems of nonlinear Schr\"odinger equations \begin{equation*} \left\{\aligned&\Delta u-(\lambda a(x)+a_0(x))u+\mu_1u^3+\beta v^2u=0\quad&\text{in }\bbr^3,\\ &\Delta v-(\lambda b(x)+b_0(x))v+\mu_2v^3+\beta u^2v=0\quad&\text{in }\bbr^3,\\ &u,v\in\h,\quad u,v>0\quad\text{in }\bbr^3,\endaligned\right. \end{equation*} where $\lambda,\mu_1,\mu_2>0$ and $\beta
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1412.7881
3
3.0
Jun 30, 2018
06/18
by
Salem Abdelmalek
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The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for m-component reaction-diffusion systems with a tridiagonal symmetric toeplitz matrix of diffusion coefficients and with nonhomogeneous boundary conditions. The proposed technique is based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1411.2116
9
9.0
Jun 30, 2018
06/18
by
Maximilian Reich
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After defining classical weighted modulation spaces we show some basic properties. In this work we additionally choose an approach in terms of the frequency-uniform decomposition and a discussion on the weights of modulation spaces leads to a definition of Gevrey-modulation spaces, where we leave the Sobolev frame and proceed to the Gevrey frame in order to get better results. We prove that Gevrey-modulation spaces are algebras under multiplication. Moreover, we obtain a non-analytic...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1411.3206
4
4.0
Jun 30, 2018
06/18
by
ALzaki Fadlallah
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The boundary value problem is examined for the system of elliptic equations of from $-\Delta u + A(x)u = 0 \quad\text{in} \Omega,$ where $A(x)$ is positive semidefinite matrix on $\mathbb{R}^{{k}\times{k}},$ and $\frac{\partial u}{\partial \nu}+g(u)=h(x) \quad\text{on} \partial\Omega$ It is assumed that $g\in C(\mathbb{R}^{k},\mathbb{R}^{k})$ is a bounded function which may vanish at infinity. The proofs are based on Leray-Schauder degree methods.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1411.3184
3
3.0
Jun 30, 2018
06/18
by
G. M. Coclite; L. di Ruvo
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We consider the Ibragimov-Shabat equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1411.5167
5
5.0
Jun 27, 2018
06/18
by
Maja Miletić; Dominik Stürzer; Anton Arnold; Andreas Kugi
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This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a nonlinear dynamic feedback system. This setup comprises nonlinear dynamic boundary controllers satisfying the nonlinear KYP lemma as well as the interaction with a nonlinear passive environment. Global-in-time wellposedness and asymptotic stability is rigorously proven for the resulting closed-loop PDE-ODE system. The analysis is based on semigroup theory for...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1505.07576
6
6.0
Jun 29, 2018
06/18
by
Lizhi Zhang; Mei Yu; Jianming He
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Let $0
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1611.09133
3
3.0
Jun 29, 2018
06/18
by
Satoshi Masaki; Hayato Miyazaki
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This paper is concerned with time global behavior of solutions to nonlinear Schr\"odinger equation with a non-vanishing condition at the spatial infinity. Under a non-vanishing condition, it would be expected that the behavior is determined by the shape of the nonlinear term around the non-vanishing state. To observe this phenomenon, we introduce a generalized version of the Gross-Pitaevskii equation, which is a typical equation involving a non-vanishing condition, by modifying the shape...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1612.02738
4
4.0
Jun 30, 2018
06/18
by
Christoph Scheven; Thomas Schmidt
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We study generalized products of divergence-measure fields and gradient measures of {\rm BV} functions. These products depend on the choice of a representative of the {\rm BV} function, and here we single out a specific choice which is suitable in order to define and investigate a notion of weak supersolutions for the $1$-Laplace operator.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1701.02656
5
5.0
Jun 30, 2018
06/18
by
H. A. Erbay; S. Erbay; A. Erkip
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We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equations. We give a precise estimate for approximation errors in terms of two small positive parameters measuring the effects of nonlinearity and dispersion. Our results demonstrate that, in the present regime, any solution of the improved Boussinesq...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1701.03491
3
3.0
Jun 30, 2018
06/18
by
Tove Dahn
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I will attempt to represent a symbol to a ps.d.o., using two bases and a lifting functional. The representation is based upon an invariance principle and conditions on the boundary, defined by first surfaces to the symbol.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1703.00515
9
9.0
Jun 30, 2018
06/18
by
Michael Pokojovy
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In the present article, we consider a thermoelastic plate of Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising from Cattaneo's law. In the absense of any additional mechanical dissipations, the system is often not even strongly stable unless restricted to the rotationally symmetric case, etc. We present a well-posedness result for the linear problem under general mixed boundary conditions for the elastic and thermal parts. For the case of a clamped, thermally isolated...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1401.5669
3
3.0
Jun 30, 2018
06/18
by
Armin Schikorra
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We introduce (integro-differential) harmonic maps into spheres, which are defined as critical points of the Besov-Slobodeckij energy $\int\limits_{\Omega}\int\limits_{\Omega} \frac{|v(x)-v(y)|^{p_s}}{|x-y|^{n+sp_s}}\ dx\ dy$. For $p_s = 2$ these are the classical fractional harmonic maps first considered by Da Lio and Riviere. For $p_s \neq 2$ this is a new energy which has degenerate, non-local Euler-Lagrange equations. For the critical case, $p_s = n/s$, we show Holder continuity of these...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1401.6854
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4.0
Jun 30, 2018
06/18
by
Enea Parini; Tobias Weth
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We consider the sublinear problem \begin {equation*} \left\{\begin{array}{r c l c} -\Delta u & = &|u|^{q-2}u & \textrm{in }\Omega, \\ u_n & = & 0 & \textrm{on }\partial\Omega,\end{array}\right. \end {equation*} where $\Omega \subset \real^N$ is a bounded domain, and $1 \leq q < 2$. For $q=1$, $|u|^{q-2}u$ will be identified with $\sgn(u)$. We establish a variational principle for least energy nodal solutions, and we investigate their qualitative properties. In...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1401.7182
3
3.0
Jun 30, 2018
06/18
by
Francesco Fanelli; Xian Liao
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The present paper is devoted to the study of a zero-Mach number system with heat conduction but no viscosity. We work in the framework of general non-homogeneous Besov spaces $B^s_{p,r}(\mathbb{R}^d)$, with $p\in[2,4]$ and for any $d\geq 2$, which can be embedded into the class of globally Lipschitz functions. We prove a local in time well-posedness result in these classes for general initial densities and velocity fields. Moreover, we are able to show a continuation criterion and a lower bound...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1403.0960
3
3.0
Jun 30, 2018
06/18
by
Francesco Fanelli; Xian Liao
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The present paper is the continuation of work [14], devoted to the study of an inviscid zero-Mach number system in the framework of \emph{endpoint} Besov spaces of type $B^s_{\infty,r}(\mathbb{R}^d)$, $r\in [1,\infty]$, $d\geq 2$, which can be embedded in the Lipschitz class $C^{0,1}$. In particular, the largest case $B^1_{\infty,1}$ and the case of H\"older spaces $C^{1,\alpha}$ are permitted. The local in time well-posedness result is proved, under an additional $L^2$ hypothesis on the...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1403.0964
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4.0
Jun 30, 2018
06/18
by
Christos Sourdis
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We prove that the energy over balls of entire, nonconstant, bounded solutions to the vector Allen-Cahn equation grows faster than $(\ln R)^k R^{n-2}$, for any $k>0$, as the volume $R^n$ of the ball tends to infinity. This improves the growth rate of order $R^{n-2}$ that follows from the general weak monotonicity formula. Moreover, our estimate can be considered as an approximation to the corresponding rate of order $R^{n-1}$ that is known to hold in the scalar case.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1404.3904
4
4.0
Jun 30, 2018
06/18
by
Claudianor O. Alves; Denilson S. Pereira
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In this work, we prove the existence of least energy nodal solution for a class of elliptic problem in both cases, bounded and unbounded domain, when the nonlinearity has exponential critical growth in $\mathbb{R}^2$. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole $\mathbb{R}^{2}$.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1404.7649
4
4.0
Jun 30, 2018
06/18
by
Moritz Egert; Robert Haller-Dintelmann; Joachim Rehberg
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We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1405.6167
3
3.0
Jun 30, 2018
06/18
by
Gennaro Infante; Mateusz Maciejewski; Radu Precup
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In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational,quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework for the existence of fixed points of nonlinear operators acting on cones that satisfy an inequality of Harnack type. Our methodology relies on fixed point index theory. We also provide a non-existence result and an example to illustrate the theory.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1401.1355
3
3.0
Jun 30, 2018
06/18
by
Yasemin Şengül; Dmitry Vorotnikov
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We study the system of equations of motion for inextensible strings. This system possesses many internal symmetries, and is related to discontinuous systems of conservation laws and the total variation wave equation. We prove existence of generalized Young measure solutions with non-negative tension after transforming the problem into a system of conservation laws and approximating it with a regularized system for which we obtain uniform estimates of the energy and the tension. We also discuss...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1401.2717
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4.0
Jun 30, 2018
06/18
by
Guy Barles; Ariela Briani; Emmanuel Chasseigne; Nicoletta Tchou
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We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control problems, the three first authors have shown that several value functions can be defined, depending, in particular, of the choice is to use only "regular strategies" or to use also "singular strategies". We study the homogenization problem in...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1405.0661
3
3.0
Jun 30, 2018
06/18
by
Ionel Sorin Ciuperca; Arnaud Heibig; Liviu Iulian Palade
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This paper establishes the existence of smooth solutions for the Doi-Edwards rheological model of viscoelastic polymer fluids in shear flows. The problem turns out to be formally equivalent to a K-BKZ equation but with constitutive functions spanning beyond the usual mathematical framework. We prove, for small enough initial data, that the solution remains in the domain of hyperbolicity of the equation for all $t \geq 0$.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1406.5325
4
4.0
Jun 30, 2018
06/18
by
Diogo A. Gomes; Hiroyoshi Mitake
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In this paper, we investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian with possibly singular congestion effects. Thanks to a new class of a-priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions.
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1407.8267
3
3.0
Jun 30, 2018
06/18
by
Juan C. Juajibioy; Richard A De la Cruz; Leonardo Rendon
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In this paper we investigate the large time behavior of the global weak entropy solutions to the symmetric Keyftiz-Kranzer system with linear damping. It is proved that as t tends to infinite the entropy solutions tend to zero in the L p norm
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1408.5856
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5.0
Jun 30, 2018
06/18
by
Andrea Davini; Albert Fathi; Renato Iturriaga; Maxime Zavidovique
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We consider a continuous coercive Hamiltonian $H$ on the cotangent bundle of the compact connected manifold $M$ which is convex in the momentum. If $u_\lambda:M\to\mathbb R$ is the viscosity solution of the discounted equation $$ \lambda u_\lambda(x)+H(x,d_x u_\lambda)=c(H), $$ where $c(H)$ is the critical value, we prove that $u_\lambda$ converges uniformly, as $\lambda\to 0$, to a specific solution $u_0:M\to\mathbb R$ of the critical equation $$ H(x,d_x u)=c(H). $$ We characterize $u_0$ in...
Topics: Mathematics, Analysis of PDEs
Source: http://arxiv.org/abs/1408.6712
3
3.0
Jun 29, 2018
06/18
by
Xinru Cao; Johannes Lankeit
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The coupled chemotaxis fluid system \begin{equation} \left\{ \begin{array}{llc} n_t=\Delta n-\nabla\cdot(n S(x,n,c)\cdot\nabla c)-u\cdot\nabla n, &(x,t)\in \Omega\times (0,T), \displaystyle c_t=\Delta c-nc-u\cdot\nabla c, &(x,t)\in\Omega\times (0,T), \displaystyle u_t=\Delta u-(u\cdot\nabla )u+\nabla P+n\nabla\Phi,\quad \nabla\cdot u=0, &(x,t)\in\Omega\times (0,T), \displaystyle \nabla c\cdot\nu=(\nabla n-nS(x,n,c)\cdot\nabla c)\cdot\nu=0, \;\; u=0,&(x,t)\in \partial\Omega\times...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1601.03897
3
3.0
Jun 29, 2018
06/18
by
Stefano Iula; Gabriele Mancini
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We study Moser-Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson-Chang type estimate by means of Onofri's inequality for the unit disk in $\mathbb{R}^2$. Moreover we consider Adimurthi-Druet type functionals on compact surfaces with conical singularities and discuss the existence of extremals for such functionals extending previous results by Cast\`o and Roy.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1601.05666
4
4.0
Jun 29, 2018
06/18
by
JiGuang Bao; HaiGang Li; YanYan Li
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We establish upper bounds on the blow-up rate of the gradients of solutions of the Lam\'{e} system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1601.07879
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4.0
Jun 29, 2018
06/18
by
Tsubasa Itoh; Hideyuki Miura; Tsuyoshi Yoneda
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We consider the two-dimensional Euler equations in non-smooth domains with corners. It is shown that if the angle of the corner $\theta$ is strictly less than $\pi/2$, the Lipschitz estimate of the vorticity at the corner is at most single exponential growth and the upper bound is sharp. %near the stagnation point. For the corner with the larger angle $\pi/2 < \theta
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1602.00815
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4.0
Jun 29, 2018
06/18
by
Joachim Krieger; Yannick Sire
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We formulate the half-wave maps problem with target $S^2$ and prove global regularity in sufficiently high spatial dimensions for a class of small critical data in Besov spaces.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1610.01216
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4.0
Jun 29, 2018
06/18
by
Davide Addona
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We consider the nonautonomous Ornstein-Uhlenbeck operator in some weighted spaces of continuous functions in $\R^N$. We prove sharp uniform estimates for the spatial derivatives of the associated evolution operator $\OU$, which we use to prove optimal Schauder estimates for the solution to some nonhomogeneous parabolic Cauchy problems associated with the Ornstein-Uhlenbeck operator. We also prove that, for any $t>s$, the evolution operator $P_{s,t}$ is compact in the previous weighted spaces.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1607.05439
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6.0
Jun 29, 2018
06/18
by
Peijun Li; Ganghua Yuan
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Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source scattering problem which is to reconstruct the source function. Our results show that increasing stability can be obtained for the inverse problem by using only the Dirichlet boundary data with multi-frequencies.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1607.06953
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3.0
Jun 29, 2018
06/18
by
Dominik Dier
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We generalize the Beurling--Deny--Ouhabaz criterion for parabolic evolution equations governed by forms to the non-autonomous, non-homogeneous and semilinear case. Let $V, H$ are Hilbert spaces such that $V$ is continuously and densely embedded in $H$ and let $\mathcal{A}(t)\colon V\to V^\prime$ be the operator associated with a bounded $H$-elliptic form $\mathfrak{a}(t,.,.)\colon V\times V \to \mathbb{C}$ for all $t \in [0,T]$. Suppose $\mathcal{C} \subset H$ is closed and convex and $P \colon...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1609.03857
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3.0
Jun 29, 2018
06/18
by
Leyter Potenciano-Machado
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In this paper we study local stability estimates for a magnetic Schr\"odinger operator with partial data on an open bounded set in dimension $n\geq 3$. This is the corresponding stability estimates for the identifiability result obtained by Bukgheim and Uhlmann $[2]$ in the presence of magnetic field and when the measurements for the Dirichlet-Neumann map are taken on a neighborhood of the illuminated region of the boundary for functions supported on a neighborhood of the shadow region. We...
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1610.04015
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3.0
Jun 29, 2018
06/18
by
Karoly J. Boroczky; Hai Trinh
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Necessary and sufficient conditions for the existence of solutions to the asymmetric $L_p$ Minkowski problem in $\mathbb{R}^2$ are established for $0 < p < 1$.
Topics: Analysis of PDEs, Mathematics
Source: http://arxiv.org/abs/1610.07067
