一类具强非线性源的半线性热方程解的性质

Some Properties of the Solutions for a Class of Semilinear Heat Equations with Strong Nonlinear Sources

讨论了具强非线性源的半线性热方程ut=△u+m in{-ε1,up}边值问题解的性质,证明了TK(uε)在L2(0,T;W10,2(Ω))中关于ε是一致有界的,且(TK(uε))t在L2(Q)中关于ε是一致有界的,从而存在一子列和一可测函数u(x,t)使得当ε→0时,uε→u a.e.于Q.其中TK(r)=m in{K,m ax(r,-K)},Q=Ω×(0,T).

This paper is devoted to the study of the semilinear heat equations of the form ut= △t＋min { ε^-1, u^p} with strong nonlinear sources. We prove that T;（u＇） is uniformly bounded in L^2（0, T; W0^1,2（Ω）） with respect to ε, （Tk（u^e））, is uniformly bounded in L^2 （Q） with respect to ε, and that there exists a subsequence of {u^e}, still indexed by ε, such that u^e→u, as ε→0, where u is a measurable function defined on Q. The truncation function is defined to be Tk（r）=min{K, max{r, -k}}, （任意） K〉0, Q=Ω （0, T）.