Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux

Abstract

This paper deals with the blow-up of the solution for a system of evolution $p$-Laplacian equations $u_{it}=\text{div}(|\nabla u_{i}|^{p-2}\nabla u_{i})\;(i=1,2,\dots,k)$ with nonlinear boundary flux. Under certain conditions on the nonlinearities and data, it is shown that blow-up will occur at some finite time. Moreover, when blow-up does occur, we obtain the upper and lower bounds for the blow-up time. This paper generalizes the previous results.

Keywords

• blow-up
• quasilinear parabolic system
• nonlinear boundary flux