Nonlocal phase-field systems with general potentials
Abstract:
We introduce a phase-field model of Caginalp type where the free energy depends on the order parameter in a nonlocal way. The resulting evolution system consists of the energy balance equation coupled with a nonlinear and nonlocal ODE for the order parameter. Such system has been analyzed by several authors, in particular when the configuration potential is a smooth double-well function. Here we consider both the case of smooth potentials as well as the case of physically realistic singular (e.g., logarithmic) potentials. We present well-posedness results and the eventual global boundedness of solutions uniformly with respect to (rather general) initial data. Also, we show that the separation property holds in the case of singular potentials. Finally, thanks to such results, we can establish the existence of a finite-dimensional global attractor. Some open issues will also be discussed.
06.12.11
09:00
Stefania Gatti
( Universita'degli Studi di Modena e Reggio, Italy )
Well-posedness and asymptotic behavior of a Caginalp model with singular potential and dynamic boundary conditions
Abstract:
This talk is devoted to the study of the well-posedness and the long time behavior of the Caginalp phase-field model with singular potentials and dynamic boundary conditions. Thanks to a suitable definition of solutions, coinciding with the strong ones under proper assumptions on the bulk and surface potentials, we are able to get dissipative estimates, leading to the existence of the global attractor with finite fractal dimension, as well as of an exponential attractor.
CZ
