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 Φ and the latent heat λ satisfy certain growth conditions.
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Dedicated to Philippe Clément
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Prüss, J., Wilke, M. (2006). Maximal L p-regularity and Long-time Behaviour of the Non-isothermal Cahn-Hilliard Equation with Dynamic Boundary Conditions. In: Koelink, E., van Neerven, J., de Pagter, B., Sweers, G., Luger, A., Woracek, H. (eds) Partial Differential Equations and Functional Analysis. Operator Theory: Advances and Applications, vol 168. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7601-5_13
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DOI: https://doi.org/10.1007/3-7643-7601-5_13
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