We consider in this article a generalization of the Caginalp model for phase transitions
based on the Maxwell Cattaneo law, instead of the classical Fourier law. In particular, we
prove the existence and uniqueness of solutions. We finally study the spatial behavior of
the solutions in a semi-infinite cylinder.
Miranville, A.; Quintanilla, R. A generalization of the Caginalp phase-field system based on the Cattaneo law. "Nonlinear analysis: theory, methods and applications", 2009, vol. 71, núm. 5-6, p. 2278-2290.