We study a phase-field system where the energy balance equation has the standard (parabolic) form, while the kinetic equation ruling the evolution of the order parameter is a nonlocal and nonlinear second-order ODE. We first prove the global existence and uniqueness of a regular solution to a suitable initial and boundary value problem associated with the system. Then, we investigate its long time behavior from the point of view of omega-limits. In particular, using a nonsmooth version of the Lojasiewicz-Simon inequality, we show that the omega-limit of any trajectory contains one and only one stationary solution, provided that the configuration potential in the kinetic equation is convex and analytic.

A nonlocal phase-field system with inertial term

SCHIMPERNA, GIULIO FERNANDO
2007-01-01

Abstract

We study a phase-field system where the energy balance equation has the standard (parabolic) form, while the kinetic equation ruling the evolution of the order parameter is a nonlocal and nonlinear second-order ODE. We first prove the global existence and uniqueness of a regular solution to a suitable initial and boundary value problem associated with the system. Then, we investigate its long time behavior from the point of view of omega-limits. In particular, using a nonsmooth version of the Lojasiewicz-Simon inequality, we show that the omega-limit of any trajectory contains one and only one stationary solution, provided that the configuration potential in the kinetic equation is convex and analytic.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/138018
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