Dynamic Properties of the p-Laplacian Reaction–Diffusion Equation in Multi-dimensional Space

In this paper we study the p -Laplacian reaction–diffusion equation u t - div ( | ∇ u | p - 2 ∇ u ) = k ( t ) f ( u ) subject to appropriate initial and boundary conditions. We show the positive solution u ( x , t ) exists globally, under the conditions on f , k and the boundary conduction function....

Full description

Saved in:
Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 20; no. 2
Main Authors Zheng, Shuai, Li, Fushan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2021
Springer Nature B.V
Subjects
Boundary conditions
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Reaction-diffusion equations
Dynamic properties
35K51
35K57
Multi-dimensional space
Time switching function
Laplacian reaction–diffusion equation
Online AccessGet full text

Cover

More Information
Summary:In this paper we study the p -Laplacian reaction–diffusion equation u t - div ( | ∇ u | p - 2 ∇ u ) = k ( t ) f ( u ) subject to appropriate initial and boundary conditions. We show the positive solution u ( x , t ) exists globally, under the conditions on f , k and the boundary conduction function. It is proved that the solution blows up at finite time, for some initial data and additional energy type conditions, by establishing accurate estimates and using the Sobolev inequality in multi-dimensional space.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-021-00494-6