On two classes of generalized viscous Cahn-Hilliard equations

Riccarda Rossi

doi:10.3934/cpaa.2005.4.405

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2005, Volume 4, Issue 2: 405-430. Doi: 10.3934/cpaa.2005.4.405

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On two classes of generalized viscous Cahn-Hilliard equations

Riccarda Rossi^1,

1.
Department of Mathematics "Felice Casorati", University of Pavia, V. Ferrata, 1 27100 Pavia

Received: February 29, 2004

Revised: November 30, 2004

Published: May 2005

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Abstract

This paper investigates two classes of generalized viscous Cahn-Hilliard equations , featuring two different laws for the mobility, which is assumed to depend on the chemical potential. Both equations can be obtained with the new derivation of equations of Cahn-Hilliard type proposed by M.E. GURTIN [14]. Approximation and compactness tools allow to prove well-posedness and, in one case, regularity results for the equations supplemented with initial and suitable boundary conditions.

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Mathematics Subject Classification: 35K60,(35D05,35B40,80A22).

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