A temperature-dependent phase segregation problem of the Allen-Cahn type
Abstract
In this paper we prove a local-in-time existence theorem for an initial-boundary value problem related to a model of temperature-dependent phase segregation that generalizes the standard Allen-Cahn's model. The problem is ruled by a system of two differential equations, one partial the other ordinary, interpreted as balances, respectively, of microforces and of microenergy, complemented by a transcendental condition on the three unknowns, that are: the order parameter entering the standard A-C equation, the chemical potential, and the absolute temperature. The results obtained by the authors in a recent paper and dealing with the isothermal case serve as a starting point for our existence proof, which relies on a fixed-point argument involving the Tychonoff-Schauder theorem.
Cite
@article{arxiv.1005.0911,
title = {A temperature-dependent phase segregation problem of the Allen-Cahn type},
author = {Pierluigi Colli and Gianni Gilardi and Paolo Podio-Guidugli and Jürgen Sprekels},
journal= {arXiv preprint arXiv:1005.0911},
year = {2010}
}
Comments
Key words: Allen-Cahn equation; integrodifferential system; temperature variable; local existence.