In this paper we consider some integro-differential systems of two parabolic PDE's coming from the Caginalp approach to phase transition models. The first (integro-differential) equation describes the evolution of the temperature and also accounts for memory effects through a memory kernel k. The latter equation, governing the evolution of the order parameter, is semilinear and of the fourth-order (in space). We prove some continuous dependence and regularity results for the solution of the Cauchy problem associated to the PDE's. Taking advantage of these results, we prove a global in time conditional existence and uniqueness result for the identification problem consisting in recovering the memory kernel k. appearing in the first equation
Direct and inverse problems for a parabolic integro-differential system of Caginalp type
SCHIMPERNA, GIULIO FERNANDO;ROCCA, ELISABETTA;
2005-01-01
Abstract
In this paper we consider some integro-differential systems of two parabolic PDE's coming from the Caginalp approach to phase transition models. The first (integro-differential) equation describes the evolution of the temperature and also accounts for memory effects through a memory kernel k. The latter equation, governing the evolution of the order parameter, is semilinear and of the fourth-order (in space). We prove some continuous dependence and regularity results for the solution of the Cauchy problem associated to the PDE's. Taking advantage of these results, we prove a global in time conditional existence and uniqueness result for the identification problem consisting in recovering the memory kernel k. appearing in the first equationI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
