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Travelling wave solutions to a semilinear diffusion system

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Esquinas, J. and Herrero, Miguel A. (1990) Travelling wave solutions to a semilinear diffusion system. Siam Journal on Mathematical Analysis , 21 (1). pp. 123-136. ISSN 0036-1410

Official URL: http://epubs.siam.org/action/showAbstract?page=123&volume=21&issue=1&journalCode=sjmaah


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Abstract

We consider the semilinear system (S) ut−uxx+vp=0, vt−vxx+uq=0(−∞<x<+∞,t>0) with p>0 and q>0. We seek nonnegative and nontrivial travelling wave solutions to (S): u(x,t)=φ(ct−x), v(x,t)=ψ(ct−x) possessing sharp fronts, i.e., such that φ(ξ)=ψ(ξ)=0 for ξ≤ξ0 and some finite ξ0, which after a phase shift can always be assumed to be located at the origin. These solutions are called finite travelling waves (FTW). Here we show that if pq<1, for any real c there exists an FTW that is unique up to phase translations and unbounded, whereas no FTW exists if pq≥1. The asymptotic wave profiles near the front as well as far from it are also determined.


Item Type:Article
Uncontrolled Keywords:Semilinear diffusion systems; travelling waves; fronts; asymptotic behaviour; travelling wave solutions; existence; uniqueness; nonexistence
Subjects:Sciences > Mathematics > Differential equations
ID Code:18091
Deposited On:31 Jan 2013 09:21
Last Modified:12 Dec 2018 15:08

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