一类非线性抛物型方程解的整体存在性和Blow-up

考虑如下的非齐次非线性抛物型方程具有正的非线性Neumann 条件的初边值问题:ut - (a(u) u)= g(u), (x , t)∈ Ψ× 0, T)un ST= f(u), (x , t)∈ S T = Ψ× 0 , T),u(x , 0)= u0(x)> 0 , x ∈ Ψ,整体解存在和解的Blow-up 行为, 解的这些行为的发生依赖于a(u), f(u), 和g(u)的相互之间所给条件.

Global Solution and Blow up for a Class of Nonlinear Parabolic Equation

In this paper , w e discuss the follow ing problem : ut - (a(u) u)= g(u), (x , t)∈ Ψ× 0, T)un ST= f(u),(x , t)∈ S T = Ψ× 0 , T),u(x , 0)= u0(x)> 0 , x ∈ Ψ,and obtain three theorems, one is about the global solution, two are about the solutio n' s blow-up phenomena .