Nonplanar Traveling Wave Solutions of Reaction-Diffusion Equations
Date Issued
2010
Date
2010
Author(s)
Chang, Yuan-Ting
Abstract
We are dealing with traveling wave solutions of a reaction-diffusion equation ut=△u+uzz-f(u), where (x, z)=(x1,---, xn, z) ∈Rn+1 is the space variable and △ is the Laplacian in Rn. Assume that f(u) is a bistable nonlinear, then we consider the balanced case and unbalanced case respectively. In the preceding case, we describe some types of traveling waves connecting two stable equilibria. In the case of latter, we want to find out the bistable-type traveling waves with the interfaces other than plane. If the solution is restricted to be cylindrically symmetric, then we can show that the interface is asymptotically a paraboloid as n≥2 and a hyperbolic cosine curve as n=1. Besides, we prove the existence of the monostable-type traveling waves. The main references of this thesis are Y. Morita, H. Ninomiya, X.F. Chen, J-S GUO, F. Hamel and J-M Roquejoffre.
Subjects
traveling wave
reaction-diffusion equation
bistable nonlinearity
interface
bistable
monostable
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