Abstract.
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.
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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
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Lorenzi, A., Rocca, E. Weak solutions for the fully hyperbolic phase-field system of conserved type. J. evol. equ. 7, 59–78 (2007). https://doi.org/10.1007/s00028-006-0235-1
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DOI: https://doi.org/10.1007/s00028-006-0235-1