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Metastable travelling-wave solutions of singularly-perturbed reaction-diffusion equations

Published online by Cambridge University Press:  01 August 1998

JACQUES G. L. LAFORGUE ,
ROBERT E. O'MALLEY  and
MICHAEL J. WARD
JACQUES G. L. LAFORGUE
Affiliation:
Departamento de Matemáticas, Universidad De Oriente, Apartado 245, Cumaná 6101A, Venezuela
ROBERT E. O'MALLEY
Affiliation:
Department of Applied Mathematics, Box 352420, University of Washington, Seattle, WA 98195, USA
MICHAEL J. WARD
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada
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Abstract

This paper determines the asymptotic solution of certain initial-boundary value problems for singularly-perturbed reaction-diffusion equations, including the Allen–Cahn and Cahn–Hilliard equations, on bounded one-dimensional spatial domains for r[ges ]0. Attention is focused on the metastable evolution of a transition layer over an asymptotically exponentially-long time interval.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 9 , Issue 4 , August 1998 , pp. 397 - 416
Copyright
1998 Cambridge University Press

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