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

中文关键词:  双重退化  初边值问题  爆破.

英文关键词:doubly degenerate  boundary value problem  blow-up.

中文摘要:

      本文研究下述双重退化抛物方程的初边值问题:$$u_t-{\rm div}(|\nabla u^m|^{p-2}\nabla u^m)=f(u),$$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.

英文摘要:

      An initial boundary value problem related to the equation $$u_t-{\rm div}(|\nabla u^m|^{p-2}\nabla u^m)=f(u)$$ 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.