Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. (English) Zbl 1133.35017

Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino; Zelik, Sergey

Math. Nachr. 280, No. 13-14, 1475-1509 (2007).

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.

Reviewer: Dumitru Motreanu (Perpignan)

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

Keywords:

strong solutions; robust exponential attractors; parabolic-hyperbolic system

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