Nonlocal time-porous medium equation: Weak solutions and finite speed of propagation

Jean-Daniel Djida; Juan J. Nieto; Iván Area

doi:10.3934/dcdsb.2019049

Article Contents

2019, Volume 24, Issue 8: 4031-4053. Doi: 10.3934/dcdsb.2019049

This issue Previous Article A remark on global solutions to random 3D vorticity equations for small initial data Next Article Stabilisation by noise on the boundary for a Chafee-Infante equation with dynamical boundary conditions

Nonlocal time-porous medium equation: Weak solutions and finite speed of propagation

1.
Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2.
Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
3.
Departamento de Matemática Aplicada Ⅱ, E.E. Aeronáutica e do Espazo, Universidade de Vigo, Campus As Lagoas s/n, 32004 Vigo, Spain

^* Corresponding author: jeandaniel.djida@usc.es
^* Corresponding author: jeandaniel.djida@usc.es

Received: March 2018

Revised: September 2018

Early access: February 2019

Published: August 2019

This work has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain under grant MTM2016–75140–P, co-financed by the European Community fund FEDER, and Xunta de Galicia, grants GRC 2015–004 and R 2016/022.

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B65, 26A33; Secondary: 35K55.

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