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Solvability of one-dimensional phase field systems associated with grain boundary motion. (English) Zbl 1270.35008
The authors investigate a system of two parabolic initial-boundary value problems, which is motivated by the phase field model of grain boundary motion, known as the Kobayashi-Warren-Carter model. They give a meaningful definition of solution to the considered system. The main result of the paper establishes the existence of solutions.

MSC:
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35K87 Unilateral problems for parabolic systems and systems of variational inequalities with parabolic operators
35R06 PDEs with measure
35K67 Singular parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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