Dynamics of Partial Differential Equations

Volume 10 (2013)

Number 4

Regularity of solutions of a phase field model

Pages: 353 – 365

DOI: http://dx.doi.org/10.4310/DPDE.2013.v10.n4.a3

Authors

T. G. Amler (Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwa, Saudi Arabia)

N. D. Botkin (Department of Mathematics, Technische Universität München, Germany)

K.-H. Hoffmann (Department of Mathematics, Technische Universität München, Germany)

K. A. Ruf (Department of Mathematics, Technische Universität München, Germany)

Abstract

Phase field models are widely-used for modelling phase transition processes such as solidification, freezing or $\mathrm{CO_2}$ sequestration. In this paper, a phase field model proposed by G. Caginalp is considered. The existence and uniqueness of solutions are proved in the case of nonsmooth initial data. Continuity of solutions with respect to time is established. In particular, it is shown that the governing initial boundary value problem can be considered as a dynamical system.

Keywords

partial differential equations, phase field model, regularity of solutions

2010 Mathematics Subject Classification

35K51, 80A22

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