退化型之反應擴散方程

Reaction-diffusion Equations of Degenerate-type

張立昇(Li-Sheng Chang)

指導教授 ： 陳俊全

國立臺灣大學/理學院/數學研究所/碩士(2005年)

https://doi.org/10.6342/NTU.2005.00840

摘要

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。

關鍵字

行波解 ； 反應擴散方程 ； 退化型 ； sharp解 ； 波速估計

並列摘要

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.

並列關鍵字

Travelling wave solutions ； Reaction-diffusion equations ； degenerate ； sharp solutions ； Speed estimates

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