Weak solutions for the fully hyperbolic phase-field system of conserved type

We consider a conserved phase-field system coupling two nonlinear hyperbolic integro-differential equations. The model results from the assumption that the material undergoing phase transition exhibits some thermal memory effects (cf. 15]) and that the response of the order parameter to the variation of the free-energy functional is delayed (cf. 10, 23]). We prove the existence of the solution to the corresponding initial-boundary value problem associated with the resulting PDE system and a (conditioned) continuous dependence estimate of the solution with respect to the data of the problem. This work is partially supported by the Italian Ministero dell’Istruzione, dell’Università e della Ricerca, PRIN no. 2004011204, Project Analisi Matematica nei Problemi Inversi