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Entire solutions of reaction—diffusion equations with balanced bistable nonlinearities

Published online by Cambridge University Press:  12 July 2007

Xinfu Chen ,
Jong-Shenq Guo  and
Hirokazu Ninomiya
Xinfu Chen
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA ([email protected])
Jong-Shenq Guo
Affiliation:
Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan ([email protected])
Hirokazu Ninomiya
Affiliation:
Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan ([email protected])
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Abstract

This paper deals with entire solutions of a bistable reaction—diffusion equation for which the speed of the travelling wave connecting two constant stable equilibria is zero. Entire solutions which behave as two travelling fronts approaching, with super-slow speeds, from opposite directions and annihilating in a finite time are constructed by using a quasi-invariant manifold approach. Such solutions are shown to be unique up to space and time translations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 6 , December 2006 , pp. 1207 - 1237
Copyright
Copyright © Royal Society of Edinburgh 2006

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