Kolmogorov-Fisher 型態的反應擴散方程
Reaction-Diffusion Equations of the Kolmogorov-Fisher Type
Date Issued
2005
Date
2005
Author(s)
Wu, Hui-Ying Chuang
DOI
zh-TW
Abstract
Wavefront solutions of scalar reaction-diffusion equations have been intensively studied for many years. There are two basic cases for the Kolmogorov-Fisher type equations, typified by a nonlinear term with simple zero root and a nonlinear term with higher order zero root. The paper is concerned with solutions u(x,t) of the equation
u_t=u_{xx}+f(u), x is in (-infty, infty)
in the case
f(u)={e^{-1/u}}*(1-u), f(1)=0, f'(1)< 0
The approach is to use the monotonicity to take u and t as
independent variables and p(u,t)=u_x(x,t) as the dependent
variable, and to apply ideas of sub- and super-solutions to the diffusion equation for p.
Subjects
反應擴散方程
Kolmogorov-Fisher Type
Type
thesis
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