Some Results on Blow-up Phenomenon for Nonlinear Porous Medium Equations with Weighted Source

This paper deals with the blow-up phenomena for a type of nonlinear porous medium equations with weighted source ut −4um = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions. Based on the auxiliary functions and differential-integral inequalities, the blow-up criterions which ensure th...

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Bibliographic Details
Published inEuropean journal of pure and applied mathematics Vol. 13; no. 3; pp. 645 - 662
Main Authors Di, Huafei, Chen, Lin, Song, Zefang
Format Journal Article
LanguageEnglish
Published 01.07.2020
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Summary:This paper deals with the blow-up phenomena for a type of nonlinear porous medium equations with weighted source ut −4um = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions. Based on the auxiliary functions and differential-integral inequalities, the blow-up criterions which ensure that u cannot exist all time are given under two different assumptions, and the corresponding estimates on the upper bounds for blow-up time and blow-up rate are derived respectively. Moreover, we use three different methods to determine the lower bounds for blow-up time and blow-up rate estimates if blow-up does occurs.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v13i3.3768