Preprint series: 06-04 , Reports on Analysis

MSC:

35K55 Nonlinear PDE of parabolic type

35B40 Asymptotic behavior of solutions

35B65 Smoothness/regularity of solutions of PDE

82C26 Dynamic and nonequilibrium phase transitions (general)

Abstract: In this paper the nonlinear Cahn-Hilliard
equation based on a microforce balance in an isotropic medium is investigated. The corresponding model was proposed by M. E. Gurtin \cite{Gur}. We show strong global well-posedness in the $L_p$ - sense. Furthermore we use the
Lojasiewicz-Simon inequality to show that each solution converges
to a steady state as time tends to infinity, as soon as the potential $\Phi$ satisfies certain growth conditions.

Keywords: Conserved order parameter, Cahn-Hilliard equation, microforce balance, Lojasiewicz-Simon inequality, convergence to steady states, optimal regularity

Upload: 2006-04-24