Blow-up of solutions for the non-Newtonian polytropic filtration equation with a generalized source
Volume 116 / 2016
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.
