In this paper we investigate quasilinear parabolic systems of conserved Penrose-Fife type. We show maximal Lp-regularity for this problem with inhomogeneous boundary data. Furthermore we prove global existence of a solution, under the assumption that the absolute temperature is bounded from below and above. Moreover, we apply the Lojasiewicz-Simon inequality to establish the convergence of solutions to a steady state as time tends to infinity.
CITATION STYLE
Prüss, J., & Wilke, M. (2011). On conserved penrose-fife type models. In Progress in Nonlinear Differential Equations and Their Application (Vol. 80, pp. 541–576). Springer US. https://doi.org/10.1007/978-3-0348-0075-4_27
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