The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions

被引：67

作者：

Biler, Piotr ^{[1
]}

Imbert, Cyril ^{[2
]}

Karch, Grzegorz ^{[1
]}

机构：

[1] Uniwersytet Wroclawski, Inst Matemat, PL-50384 Wroclaw, Poland

[2] Univ Paris Est Creteil, CNRS, UMR 8050, F-94010 Creteil, France

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2015年 / 215卷 / 02期

关键词：

PRINCIPLE;

D O I：

10.1007/s00205-014-0786-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A degenerate nonlinear nonlocal evolution equation is considered; it can be understood as a porous medium equation whose pressure law is nonlinear and nonlocal. We show the existence of sign-changing weak solutions to the corresponding Cauchy problem. Moreover, we construct explicit compactly supported self-similar solutions which generalize Barenblatt profiles-the well-known solutions of the classical porous medium equation.

引用

页码：497 / 529

页数：33

共 33 条

[1] APPLICATION OF THE INVARIANCE PRINCIPLE TO REACTION-DIFFUSION EQUATIONS [J].

ALIKAKOS, ND .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1979, 33 (02) :201-225

[2] Regularity of solutions of the fractional porous medium flow [J].

不详 .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2013, 15 (05) :1701-1746

[3]

[Anonymous], 1971, Princeton Mathematical Series

[4]

[Anonymous], 1970, SINGULAR INTEGRALS D

[5] On the Dirichlet problem for second-order elliptic integro-differential equations [J].

Barles, G. ;

Chasseigne, E. ;

Imbert, C. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (01) :213-246

[6]

Biler P., FINITE SPEED PROPAGA

[7] Barenblatt profiles for a nonlocal porous medium equation [J].

Biler, Piotr ;

Imbert, Cyril ;

Karch, Grzegorz .

COMPTES RENDUS MATHEMATIQUE, 2011, 349 (11-12) :641-645

[8] 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

[9] Nonlinear Porous Medium Flow with Fractional Potential Pressure [J].

Caffarelli, Luis ;

Vazquez, Juan Luis .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 202 (02) :537-565

[10] ASYMPTOTIC BEHAVIOUR OF A POROUS MEDIUM EQUATION WITH FRACTIONAL DIFFUSION [J].

Caffarelli, Luis A. ;

Luis Vazquez, Juan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 29 (04) :1393-1404

← 1 2 3 4 →