A hyperbolic integrodifferential system related to phase-field models (Q2733859)

The paper deals with a system of two nonlinear integro-partial differential equations of hyperbolic type. The equations have convolution terms which come into play when the usual Fourier heat conduction law is replaced by the linearized Gurtin-Pipkin constitutive assumption, see \textit{M. E. Gurtin} and \textit{A. C. Pipkin} [Arch. Ration. Mech. Anal. 31, 113-126 (1968; Zbl 0164.12901)]. From a physical point of view in such a system both the temperature and the phase-field propagate at finite speed. Sufficient conditions are given when the Cauchy-Neumann problem associated with the considered evolution system admits a unique generalized solution which depends continuously on the data. The existence of variational solutions for the above problem is established. NEWLINENEWLINENEWLINEIn this connection we also mention the papers by \textit{S. Aizicovici} and \textit{V. Barbu} [NoDEA, Nonlinear Differ. Equ. Appl. 3, No. 1, 1-18 (1996; Zbl 0844.35040)] and \textit{P. Colli} and \textit{P. Laurencot} [J. Integral Equations Appl. 10, No. 2, 169-194 (1998; Zbl 0925.45006); J. Math. Sci., Tokyo 5, No. 3, 459-476 (1998; Zbl 0933.35103)].