In this paper, we prove the existence and global boundedness from above for a solution to an integro-differential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integro-differential inclusion governing the (vectorial) phase-parameter dynamics. The specific heat and the heat conductivity k are allowed to depend both on the order parameter ? and on the absolute temperature ? of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions.
A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity
P Colli;E Rocca;
2011
Abstract
In this paper, we prove the existence and global boundedness from above for a solution to an integro-differential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integro-differential inclusion governing the (vectorial) phase-parameter dynamics. The specific heat and the heat conductivity k are allowed to depend both on the order parameter ? and on the absolute temperature ? of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.