On two classes of generalized viscous Cahn-Hilliard equations

Pages: 405 - 430, Volume 4, Issue 2, June 2005

doi:10.3934/cpaa.2005.4.405       Abstract        Full Text (393.6K)       Related Articles

Riccarda Rossi - Department of Mathematics "Felice Casorati", University of Pavia, V. Ferrata, 1 27100 Pavia, Italy (email)

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.

Keywords:  Viscous Cahn-Hilliard equation, micro force balance, Neumann and Robin boundary conditions.
Mathematics Subject Classification:  35K60,(35D05,35B40,80A22)

Received: March 2004;      Revised: December 2004;      Published: March 2005.