Blow-up of p-laplace heat equation on riemannian manifolds

Abstract

Let M be an n-dimensional smooth manifold with boundary [สูตร] . Consider the initial-boundary value problems of the form [สูตร] where ∆p is the p-Laplace-Beltrami operator. We obtain conditions of the initial function u₀ in which the classical solution of the problem blows up in a finite time.