一个反应扩散方程局部解的存在性

The existence of local solutions of a reaction-diffusion equation

主要研究了一个由反应扩散方程推出的含有参数τ和γ的抛物型自由边界问题.我们已经证明了当τ和γ均充分大时,该问题的解在(0,+∞)内存在.本文主要证明当γ充分大、τ充分小时,该问题存在局部解,即该解在有限的时间范围[0,T*]内存在.

In this paper we study a free boundary problem of parabolic equations with positive parameters γ and τ which arises from some reaction - diffusion system. We have proved the solution exists for 0 〈 t 〈 ＋ when the γ and τ are large enough. Now we prove that, if γ is large enough while γ is small enough, the solution exists for 0 〈 t 〈 T^＊.