We consider a phase-eld system modeling phase transition phe- nomena, where the Cahn{Hilliard{Oono equation for the order parameter is coupled with the Coleman{Gurtin heat law for the temperature. The former suitably describes both local and nonlocal (long-ranged) interactions in the material undergoing phase-separation, while the latter takes into account ther- mal memory eects. We study the well-posedness and longtime behavior of the corresponding dynamical system in the history space setting, for a class of physically relevant and singular potentials. Besides, we investigate the reg- ularization properties of the solutions and, for suciently smooth data, we establish the strict separation property from the pure phases.
A SINGULAR CAHN-HILLIARD-OONO PHASE-FIELD SYSTEM WITH HEREDITARY MEMORY
M. Conti;
2018-01-01
Abstract
We consider a phase-eld system modeling phase transition phe- nomena, where the Cahn{Hilliard{Oono equation for the order parameter is coupled with the Coleman{Gurtin heat law for the temperature. The former suitably describes both local and nonlocal (long-ranged) interactions in the material undergoing phase-separation, while the latter takes into account ther- mal memory eects. We study the well-posedness and longtime behavior of the corresponding dynamical system in the history space setting, for a class of physically relevant and singular potentials. Besides, we investigate the reg- ularization properties of the solutions and, for suciently smooth data, we establish the strict separation property from the pure phases.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
