an:05155341
Zbl 1120.35024
Wu, Hao; Grasselli, Maurizio; Zheng, Songmu
Convergence to equilibrium for a parabolic-hyperbolic phase-field system with Neumann boundary conditions
EN
Math. Models Methods Appl. Sci. 17, No. 1, 125-153 (2007).
00192524
2007
j
35B40 80A22
Simon-Lojasiewicz inequality; real analytic nonlinearities
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.
Peter Pol????ik (Minneapolis)