$L_p$-theory for a Cahn-Hilliard-Gurtin system

Details $L_p$-theory for a Cahn-Hilliard-Gurtin system $L_p$-theory for a Cahn-Hilliard-Gurtin system

2012-03-20

arxiv.org/abs/1203.4391v1

Mathematics

Analysis of PDEs

38 pages

Scientific paper

In this paper we study a generalized Cahn-Hilliard equation which was proposed by Gurtin. We prove the existence and uniqueness of a local-in-time solution for a quasilinear version, that is, if the coefficients depend on the solution and its gradient. Moreover we show that local solutions to the corresponding semilinear problem exist globally as long as the physical potential satisfies certain growth conditions. Finally we study the long-time behaviour of the solutions and show that each solution converges to a equilibrium as time tends to infinity.

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