奇异半线性反应扩散方程组Cauchy问题

CAUCHY PROBLEM OF SINGULAR SEMILINEAR REACTION-DIFFUSION SYSTEM

本文讨论如下问题其中σ>0,Pi>1,qi>1(i=1,2),α1≥0,α2>0,β1>0,β2≥0,fi(x)(i=1,2)连续有界非负, (f1(x),f2(x))(?)(0,0).给出了非负局部解存在的几个充分条件和解的爆破结果.

This paper discusses the following problem:where σ > 0, pi > 1, qi > 1 (i = 1,2), α1≥0, α2 > 0, β1 > 0,β2≥ 0, fi(x) (i = 1,2) are nonnegative, bounded and continuous, (f1(x),f2(x))(?)(0,0). Sufficient conditions for the existence of nonnegative local solutions and conditions for blow-up are established.