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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
