Global solution and long-time behavior for a problem of phase segregation of the Allen-Cahn type

Details Global solution and long-time behavior for a problem of phase segregation of the Allen-Cahn type Global solution and long-time behavior for a problem of phase segregation of the Allen-Cahn type

2009-02-27

arxiv.org/abs/0902.4741v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we study a model for phase segregation consisting in a sistem
of a partial and an ordinary differential equation. By a careful definition of
maximal solution to the latter equation, this system reduces to an Allen-Cahn
equation with a memory term. Global existence and uniqueness of a smooth
solution are proven and a characterization of the omega-limit set is given.

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