NONLOCAL TIME-POROUS MEDIUM EQUATION: WEAK SOLUTIONS AND FINITE SPEED OF PROPAGATION

被引：11

作者：

Djida, Jean-Daniel ^{[1
]}

Nieto, Juan J. ^{[2
,3
]}

Area, Ivan ^{[2
,3
]}

机构：

[1] Univ Santiago de Compostela, Dept Estat Analise Matemat & Optimizac, Santiago De Compostela 15782, Spain

[2] Univ Santiago de Compostela, Dept Estat Analise Matemat & Optimizac, Inst Matemat, Santiago De Compostela 15782, Spain

[3] Univ Vigo, Dept Matemat Aplicada 2, EE Aeronaut & Espazo, Campus As Lagoas S-N, Vigo 32004, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2019年 / 24卷 / 08期

关键词：

Nonlinear fractional diffusion; fractional Laplacian; fractional derivatives; existence of weak solutions; finite speed of propagation; free boundary; PARABOLIC PROBLEM; INFINITE SPEED; DIFFUSION; BEHAVIOR;

D O I：

10.3934/dcdsb.2019049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a fractional time porous medium equation with fractional potential pressure. The initial data is assumed to be a bounded function with compact support and fast decay at infinity. We establish existence of weak solutions for which we determine whether the property of compact support is conserved in time depending on some parameters of the problem. Special attention is paid to the property of finite propagation for specific values of the parameters.

引用

页码：4031 / 4053

页数：23

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