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 9812566503

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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, timedependent 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 

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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