Electron. J. Diff. Eqns., Vol. 2004(2004), No. 126, pp. 1-24.

A generalized solution to a Cahn-Hilliard/Allen-Cahn system

Jose Luiz Boldrini, Patricia Nunes da Silva

Abstract:
We study a system consisting of a Cahn-Hilliard and several Allen-Cahn type equations. This system was proposed by Fan, L.-Q. Chen, S. Chen and Voorhees for modelling Ostwald ripening in two-phase system. We prove the existence of a generalized solution whose concentration component is in $L^{\infty}$.

Submitted June 10, 2004. Published October 25, 2004.
Math Subject Classifications: 47J35, 35K57, 35Q99.
Key Words: Cahn-Hilliard and Allen-Cahn equations; Ostwald ripening; phase transitions

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José Luiz Boldrini
DM-IMECC-UNICAMP, CP 6065
13083-970 Campinas, SP, Brazil
email: boldrini@ime.unicamp.br
Patrícia Nunes da Silva
DM-IME-UERJ
Rio de Janeiro, RJ, Brazil
email: nunes@ime.uerj.br

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