Preprint series: 05-03, 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 we investigate the nonlinear Cahn-Hilliard
equation with nonconstant temperature and dynamic boundary
conditions. We show maximal $L_p$ - regularity for this problem
with inhomogeneous boundary data. Furthermore we show global existence and 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 $\Phi$ and the latent heat $\la$ satisfy certain growth conditions.

Keywords: Conserved phase field models, Cahn-Hilliard equation, dynamic boundary condition, maximal regularity, Lojasiewicz-Simon inequality, convergence to steady states

Upload: 2005-04-05

Update: 2005 -04 -05