Norbury, John and Girardet, Christophe (2006) *Gradient flow reaction/diffusion models in phase transitions.* In: Dissipative Phase Transitions. Series on Advances in Mathematics for Applied Sciences, 71 . World Scientific. ISBN 981-256-650-3

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## Abstract

In this article we consider a nonlinear large reaction small diffusion problem which has two (or more) stable states, and we analyse it using two different methods.

First method: an approach based on (asymptotic) expansions; and second method: an approach based on the notion of -convergence.

The analysis of such a problem shows that the two methods are complementary. It is well known that, for such a problem, time-dependent solutions are characterised by (moving) layers or vortices. Here, we are specially interested in the existence, the shape and the motion of such layers or vortices, with respect to the inhomogeneous coefficients appearing in the problem as well as the domain . We generalise, in the limit of small diffusion, the usual motion by mean curvature laws found for homogeneous problems.

Item Type: | Book Section |
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Subjects: | O - Z > Partial differential equations |

Research Groups: | Oxford Centre for Industrial and Applied Mathematics |

ID Code: | 305 |

Deposited By: | Gareth Wyn Jones |

Deposited On: | 27 Oct 2006 |

Last Modified: | 20 Jul 2009 14:20 |

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