Abstract:
Caginalp phase-field model describes the behaviour of certains materials in their stages of melting and solidication. In this talk, we will start by motivating the use of Cattaneo's law and give a rigourous derivation of our model. We then address mathematical problems of existence and uniqueness, dissipativity and spatial behaviour in a semi-infinite cylinder. We finally give the convergence for an iterative scheme of fractional steps type associated to the phase-field transition system as an illustration regarding numerical approach.