Well-posedness and Long Time Behavior of a Parabolic-hyperbolic Phase-field System with Singular Potentials
نویسندگان
چکیده
In this article, we study the long time behavior of a phase-field parabolichyperbolic system arising from the phase-field theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equation ruling the evolution of the order parameter. The latter is a singular perturbation through an inertial term of the parabolic Allen-Cahn equation and it is characterized by the presence of a singular potential, e.g., of logarithmic type, instead of the classical double-well potential. We first prove the existence and uniqueness of strong solutions when the inertial coefficient ε is small enough. Then, we construct a robust family of exponential attractors (as ε goes to 0). Introduction We consider the following parabolic-hyperbolic system in a bounded smooth domain Ω ⊂ R:
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تاریخ انتشار 2007