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Convergence to travelling fronts in semilinear parabolic equations

Published online by Cambridge University Press:  14 November 2011

Franz Rothe
Franz Rothe
Affiliation:
Lehrstuhl für Biomathematik, Universität Tubingen
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Synopsis

We study the convergence to the stationary state for the parabolic equation u, = uxx + F(u). There exist wave-type solutions u(x, t) = φ(x − ct) for a continuum of velocities c. In the asymptotic behavior of this equation was investigated for a step function as initial data. In this paper we obtain the asymptotic behavior for a large class of monotone initial data.

All solutions with initial data in this class evolve to wave-type solutions, where the rate of decay of the initial data determines the asymptotic speed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 3-4 , 1978 , pp. 213 - 234
Copyright
Copyright © Royal Society of Edinburgh 1978

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