Front motion for phase transitions in systems with memory
摘要
We consider the Allen-Cahn equations with memory (a partial integro-differential convolution equation). The prototype kernels are exponentially decreasing functions of time and they reduce the integrodifferential equation to a hyperbolic one, the damped Klein-Gordon equation. By means of a formal asymptotic analysis we show that to the leading order and under suitable assumptions on the kernels, the integro-differential equation behave like a hyperbolic partial differential equation obtained by considering prototype kernels: the evolution of fronts is governed by the extended, damped Born-Infeld equation. We also apply our method to a system of partial integro-differential equations which generalize the classical phase field equations with a non-conserved order parameter and describe the process of phase transitions where memory effects are present.
引用
@article{arxiv.nlin/0002039,
title = {Front motion for phase transitions in systems with memory},
author = {Horacio G. Rotstein and Alexander I. Domoshnitsky and Alexander Nepomnyashchy},
journal= {arXiv preprint arXiv:nlin/0002039},
year = {2016}
}