一类非线性反应扩散方程组的定性分析

Qualitative Analysis of a Quasilinear Reaction-diffusion System

考虑一类非线性反应扩散方程组初边值问题解的整体存在性,爆破及稳定性等。通过构造上下解,利用比较原理得到了一些关于解的整体存在性和爆破的一些充分条件,同时给出了平凡定态解的局部稳定性。

In this paper, the global existence, blow-up, stability etc for a quasilinear reaction-diffusion system with homogeneous Dirichlete boundary data are discussed. Under appropriate hypotheses, the local stability of the trivial steady state, as well as solutions either exists globally or the blow-up behavior by utilizing sub and super solutions techniques and comparison principle are obtained.