Abstract
Here we study a nonlinear hyperbolic integrodifferential system which was proposed by H.G. Rotstein et al. to describe certain peculiar phase transition phenomena. This system governs the evolution of the (relative) temperature ϑ and the order parameter (or phase-field) χ. We first consider an initial and boundary value problem associated with the system and we frame it in a history space setting. This is done by introducing two additional variables accounting for the histories of ϑ and χ. Then we show that the reformulated problem generates a dissipative dynamical system in a suitable infinite-dimensional phase space. Finally, we prove the existence of a universal attractor.
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Grasselli, M., Pata, V. Existence of a universal attractor for a fully hyperbolic phase-field system. J.evol.equ. 4, 27–51 (2004). https://doi.org/10.1007/s00028-003-0074-2
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DOI: https://doi.org/10.1007/s00028-003-0074-2