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Existence of a universal attractor for a parabolic-hyperbolic phase-field system. (English) Zbl 1057.37068
The authors consider a nonconserved parabolic-hyperbolic phase field system for temperature and order parameter evolution on a bounded smooth domain in three-space. They prove existence of a universal attractor in an appropriate phase space for homogeneous Dirichlet and Neumann boundary conditions for the two components respectively, and Lipschitz continuous nonlinearities. They compare this to the standard phase field system.

37L30 Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents
35B41 Attractors
35L70 Second-order nonlinear hyperbolic equations
35K55 Nonlinear parabolic equations