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Convergence to equilibrium for a parabolic-hyperbolic phase-field system with Neumann boundary conditions. (English) Zbl 1120.35024
The paper is concerned with the asymptotic behavior of solutions to a parabolic-hyperbolic coupled system which describes the evolution of the relative temperature \(\theta\) and the order parameter \(\chi\) in a material subject to phase transitions. Neumann boundary condition for both \(\theta\) and \(\chi\) are assumed and the nonlinearities in the equation are assumed real analytic. Employing a suitable Simon-Lojasiewicz inequality the authors prove the convergence of global solutions to an equilibrium.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
80A22 Stefan problems, phase changes, etc.
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