Maximal Lp-regularity and Long-time Behaviour of the Non-isothermal Cahn-Hilliard Equation with Dynamic Boundary Conditions
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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
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