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Development of interfaces in ℝN

Published online by Cambridge University Press:  14 November 2011

P. de Mottoni  and
M. Schatzman
P. de Mottoni
Affiliation:
Dipartimento di Matematica, Universitá di Roma – Tor Vergata, I-00173 ROMA –, Italy
M. Schatzman
Affiliation:
Laboratoire d'Analyse Numérique, Université Lyon 1, 43 bd du 11 novembre 1918, 69622 Villeurbanne Cedex, France
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Abstract

Consider the reaction-diffusion equation in ℝN × ℝ+: ut − h2 Δu + Φ(u) = 0, where Φ is the derivative of a bistable even potential, and h is a small parameter. If the initial data have a smooth noncritical zero set, we prove that an interface appears in time O(log (h−1)), and that the solution stays close to it for at least time O(1/√h).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 3-4 , 1990 , pp. 207 - 220
Copyright
Copyright © Royal Society of Edinburgh 1990

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