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June  2005, 4(2): 405-430. doi: 10.3934/cpaa.2005.4.405

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, Italy

Received  March 2004 Revised  December 2004 Published  March 2005

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.
Keywords: Viscous Cahn-Hilliard equation, micro force balance, Neumann and Robin boundary conditions..
Mathematics Subject Classification: 35K60,(35D05,35B40,80A22).
Citation: Riccarda Rossi. On two classes of generalized viscous Cahn-Hilliard equations. Communications on Pure & Applied Analysis, 2005, 4 (2) : 405-430. doi: 10.3934/cpaa.2005.4.405
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