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Travelling waves in an initial-boundary value problem

Published online by Cambridge University Press:  14 November 2011

E. J. M. Veling
E. J. M. Veling
Affiliation:
Mathematical Centre, 49, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
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Synopsis

In this paper we consider the initial-boundary value problem for the semihnear diffusion equation ul=uxx+f(u) on the half-line x>0, when for 0<a<1 f(0)=f(a)=f(1)=0 and f(u)<0 on (0, a), f(u)>0 on (a, 1). For a wide class of initial and boundary values a uniformly valid asymptotic expression is given to which the solution converges exponentially. This expression is composed of a travelling wave and a solution of the stationary problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 41 - 61
Copyright
Copyright © Royal Society of Edinburgh 1981

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