退化型之反應擴散方程

Abstract

這篇論文討論反應擴散方程在Fisher-KPP及bistable的情形下擴散係數退化所造成的影響。當非線性項是Fisher-KPP時，我們可得到一連串波速c≧c*的行波解，其中波速c=c*時會產生sharp的行波解；當非線性項是bistable時發現所有行波解均為sharp。最後我們利用Min-max方法去估計出sharp行波解之波速。

This paper investigates the effects of a degenerate diffusion term in reaction-diffusion models with Fisher-KPP and bistable type nonlinearities. In the first case when the nonlinear term g is of Fisher-KPP type, we obtain a continuum of t.w.s. having wave speed c greater than a threshold value c* and the appearance of a sharp-type profile if c = c*. In the other case when g is bistable, we observe that the t.w.s. is of sharp type. Finally, we estimate the speed of front propagation for reaction-diffusion equations. This formulation makes it possible to calculate sharp estimates for the speed explicitly.