The Mathematical Institute, University of Oxford, Eprints Archive

Gradient flow reaction/diffusion models in phase transitions

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



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 $\Gamma$-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 $\Omega$. We generalise, in the limit of small diffusion, the usual motion by mean curvature laws found for homogeneous problems.

Item Type:Book Section
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:29 May 2015 18:19

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