Stability of the interface in a model of phase separation
- 1 January 1994
- journal article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 124 (5) , 1013-1022
- https://doi.org/10.1017/s0308210500022472
Abstract
The paper is concerned with the asymptotic behaviour of the solutions to a nonlocal evolution equation which arises in models of phase separation. As in the Allen–Cahn equations, stationary spatially nonhomogeneous solutions exist, which represent the interface profile between stable phases. Local stability of these interface profiles is proved.This publication has 6 references indexed in Scilit:
- Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scalesNonlinearity, 1994
- A mean-field equation of motion for the dynamic Ising modelJournal of Statistical Physics, 1991
- Bounds on the 𝐿² spectrum for Markov chains and Markov processes: a generalization of Cheeger’s inequalityTransactions of the American Mathematical Society, 1988
- On secondary bifurcations for some nonlinear convolution equationsTransactions of the American Mathematical Society, 1986
- The approach of solutions of nonlinear diffusion equations to travelling front solutionsArchive for Rational Mechanics and Analysis, 1977
- Rigorous Treatment of the Van Der Waals-Maxwell Theory of the Liquid-Vapor TransitionJournal of Mathematical Physics, 1966