## 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.

### MSC:

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

### Keywords:

nonconserved phase field system; universal attractor