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Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. (English) Zbl 1133.35017
The paper studies a nonlinear coupled parabolic-hyperbolic system motivated by phase-field models which depend of a small parameter. Different results in the paper provide information about the limit parabolic system, uniform a priori estimates, existence of solutions and robust exponential attractors.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
80A22 Stefan problems, phase changes, etc.
35B41 Attractors
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