On the behavior of the solutions of certain nonlinear parabolic problems (Spanish: Sobre el comportamiento de las soluciones de ciertos problemas parabólicos no lineales)

Abstract

For 1<p<∞ let Δpu=∑ni=1Dxi(|Dxiu|p−2Dxiu). Consider the initial value problem (∗) ut−Δpu+β(u)=0 for (x,t)∈Rn×[0,T], u(0)=u0(x) for x∈Rn. Here β is a continuous, nondecreasing real function such that β(0)=0. The author obtains sufficient conditions for the existence of both finite extinction time and compact support in x for solutions of (∗). Some counterexamples are given when the conditions are removed.