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Existence and uniqueness results to a phase transition model based on microscopic accelerations and movements. (English) Zbl 1092.80006
Microscopic movements give rise to phase transition at the macroscopic level and if not neglected lead to nonlinear parabolic-hyperbolic Cauchy-Neumann problems. The local existence and uniqueness of a solution of these problems is presented through two well-posedness results.
The proof of the first is based on a fixed point argument, while the second is based on techniques based on a priori estimates.

MSC:
80A22 Stefan problems, phase changes, etc.
35K55 Nonlinear parabolic equations
35L70 Second-order nonlinear hyperbolic equations
35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators
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