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arXiv · nlin/0002039

Front motion for phase transitions in systems with memory

Horacio G. Rotstein·Alexander I. Domoshnitsky·Alexander Nepomnyashchy
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Abstract

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.

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Horacio G. Rotstein, Alexander I. Domoshnitsky, Alexander Nepomnyashchy. 2000-02-22. Front motion for phase transitions in systems with memory. https://doi.org/10.1016/s0167-2789(00)00132-9

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