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Blow-up of solutions for the non-Newtonian polytropic filtration equation with a generalized source

Volume 116 / 2016

Jun Zhou Annales Polonici Mathematici 116 (2016), 197-216 MSC: Primary 35K55; Secondary 35K65. DOI: 10.4064/ap3788-10-2015 Published online: 24 February 2016

Abstract

This paper deals with the blow-up properties of the non-Newtonian polytropic filtration equation $$ u_t-{\rm div}(|\nabla u^m|^{p-2}\nabla u^m)=f(u) $$ with homogeneous Dirichlet boundary conditions. The blow-up conditions, upper and lower bounds of the blow-up time, and the blow-up rate are established by using the energy method and differential inequality techniques.

Authors

  • Jun ZhouSchool of Mathematics and Statistics
    Southwest University
    Chongqing, 400715, P.R. China
    e-mail

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