SINGULAR SOLUTION OF A QUASILINEAR CONVECTION DIFFUSION DEGENERATE PARABOLIC EQUATION WITH ABSORPTION

• 来源期刊: 偏微分方程(英文版)
• 学科: 数学
• 关键词: Convect diffusion equation Cauchy problem non-trivial solution
• 年，卷（期）: 2007,（4）
• 页码范围: 349-364
• 页数: 16页
• 分类号: O175.26
• 语种: 英文

摘要

In this paper the existence and nonexistence of non-trivial solution for the Cauchy problem of the form ｛ut=div(｜▽u｜p-2▽u)-(σ)/(σ)xibi(u)-uq,u(x,O)=O,(x,t)∈ST=RN×(O,T),x∈RN\｛O｝are studied. We assume that ｜b'i(s)｜≤Msm-1, and proved that if P＞2, 0＜q＜p-1+p/N,0≤m＜p-1+p/N, then the problem has a solution;if p＞2, q＞p-1+p/N,O≤m≤q(p+Np-N-1)/p+Np-N, then the problem has no solution;if p＞2,p-1＜q＜p-1+p/N,0≤m＜q, then the problem has a very singular solution;if p＞2,q＞p-1+p/N, 0＜m＜q-p/2N,then the problem has no very singular solution.We use P.D.E.methods such as regularization,Moser iteration and Imbedding Theorem.