BLOWUP AND EXISTENCE OF GLOBAL SOLUTIONS TO NONLINEAR PARABOLIC EQUATIONS WITH DEGENERATE DIFFUSION

被引：0

作者：

Zhang, Zhengce ^{[1
]}

Li, Yan ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年

基金：

中国国家自然科学基金;

关键词：

Degenerate parabolic equation; L-infinity blowup; gradient blowup; global solution; comparison principle; GRADIENT BLOWUP; HEAT-EQUATION; P-LAPLACIAN; NONEXISTENCE; CONVERGENCE; BOUNDARY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the degenerate parabolic equation u(t) - div(vertical bar del u vertical bar(p-2)del u) = lambda u(m) + mu vertical bar del u vertical bar(q) on a smoothly bounded domain Omega subset of R-N (N >= 2), with homogeneous Dirichlet boundary conditions. The values of p > 2, q; m; lambda and mu will vary in different circumstances, and the solutions will have different behaviors. Our main goal is to present the sufficient conditions for L-infinity blowup, for gradient blowup, and for the existence of global solutions. A general comparison principle is also established.

引用

页数：17

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