Weak solutions of fractional differential equations in non cylindrical domains

被引：17

作者：

Kubica, A. ^{[1
]}

Rybka, P. ^{[2
]}

Ryszewska, K. ^{[1
]}

机构：

[1] Warsaw Univ Technol, Dept Math & Informat Sci, Ul Koszykowa 75, PL-00662 Warsaw, Poland

[2] Warsaw Univ, Inst Appl Math & Mech, Ul Banacha 2, PL-02097 Warsaw, Poland

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2017年 / 36卷

关键词：

Time fractional Caputo derivative; Heat equation; Galerkin method;

D O I：

10.1016/j.nonrwa.2017.01.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a time fractional heat equation in a non cylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：154 / 182

页数：29

共 12 条

[1]

[Anonymous], 2004, Lecture Notes in Mathematics

[2]

[Anonymous], 2006, Journal of the Electrochemical Society

[3] Critical nonlinearity exponent and self-similar asymptotics for Levy conservation laws [J].

Biler, P ;

Karch, G ;

Woyczynski, WA .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2001, 18 (05) :613-637

[4] Nonlinear Diffusion of Dislocation Density and Self-Similar Solutions [J].

Biler, Piotr ;

Karch, Grzegorz ;

Monneau, Regis .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 294 (01) :145-168

[5]

Foufoula-Georgiou E., 2010, J. Geophys. Res, V115, pF00A16

[6]

Gariepy RF., 1992, MEASURE THEORY FINE

[7]

Klafter J., 2011, First Steps in RandomWalks: From Tools to Applications

[8]

Samko A. A., 1993, Fractional Integrals andDerivatives: Theory and Applications

[9] Fractional advection-dispersion equations for modeling transport at the Earth surface [J].

Schumer, Rina ;

Meerschaert, Mark M. ;

Baeumer, Boris .

JOURNAL OF GEOPHYSICAL RESEARCH-EARTH SURFACE, 2009, 114

[10] Moving boundary problems governed by anomalous diffusion [J].

Vogl, Christopher J. ;

Miksis, Michael J. ;

Davis, Stephen H. .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2012, 468 (2147) :3348-3369

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