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.
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页数：17
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