Maximal Lp-regularity and Long-time Behaviour of the Non-isothermal Cahn-Hilliard Equation with Dynamic Boundary Conditions
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 Φ and the latent heat λ satisfy certain growth conditions.
KeywordsConserved phase field models Cahn-Hilliard equation dynamic boundary condition maximal regularity Lojasiewicz-Simon inequality convergence to steady states
Unable to display preview. Download preview PDF.
- Chill, R.; Fašangová, E.; Prüss, J. Convergence to steady states of solutions of the Cahn-Hilliard equation with dynamic boundary conditions. Math. Nachr. 2005, to appear.Google Scholar
- Denk, R.; Hieber, M.; Prüss, J. Optimal L p — L q-Regularity for Parabolic Problems with Inhomogeneous Boundary Data. Submitted, 2005.Google Scholar
- Prüss, J.; Racke, R.; Zheng, S. Maximal Regularity and Asymptotic Behavior of Solutions for the Cahn-Hilliard Equation with Dynamic Boundary Conditions. Annali Mat. Pura Appl. 2005, to appear.Google Scholar
- Triebel, H. Theory of Function Spaces I, II. Birkhäuser, Basel, 1983, 1992.Google Scholar
- Zacher, R. Quasilinear parabolic problems with nonlinear boundary conditions. Ph.D.-Thesis, Halle, 2003.Google Scholar