一类退缩抛物型偏微分方程组解的加权L_1模的有界性及爆破性

Blow-up and boundedness in a weighted norm to the solutions of a degenerate system of parabolic equations

利用Laplace方程第一特征值及特征函数,定义了可积函数的加权模并用之研究了所讨论的具退缩性或奇性非线性反应-扩散方程组非负解的爆破性和全局有界性.

This article deals with a system of nonlinear reaction-diffusion equations with degeneracy or singularities by using the first eigenvalue and the corresponding eigenfunction to the Laplacian equation. It is shown that if the nonlinear terms in the system grow fast, the solution will blow up in a finite time and if the nonlinear terms in the system grow in a reasonable speed, the solution will be bounded in any finite time.