Mathematics – Analysis of PDEs
Scientific paper
2010-05-06
Mathematics
Analysis of PDEs
Key words: Allen-Cahn equation; integrodifferential system; temperature variable; local existence.
Scientific paper
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.
Colli Pierluigi
Gilardi Gianni
Podio-Guidugli Paolo
Sprekels Jürgen
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