一类双重退化抛物方程解的存在性及零初始能量下的爆破

Existence of Solutions to a Class of Doubly Degenerate Equations and Blow up with Vanishing Initial Energy

本文研究下述双重退化抛物方程的初边值问题:并证明在f满足适当的条件下具零或者负初始能量的解的存在性和在有限时刻的爆破性结果.

An initial boundary value problem related to the equation ut-div（｜△↓u^m｜^p-2△↓u^m）=f（u） is studied in this paper. We prove, under suitable conditions on f, a blow up result for solutions with vanishing or negative initial energy. The existence of solutions is also given.