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On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law Miranville, Alain Quintanilla de Latorre, Ramón Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals Thermoelasticity Caginalp systems Maxwell-Cattaneo law Two temperatures Well-posedness Dissipativity Equacions diferencials parcials Calor -- Transmissió Termoelasticitat Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type Classificació AMS::80 Classical thermodynamics, heat transfer::80A Thermodynamics and heat transfer This is the peer reviewed version of the following article: Miranville, A., and Quintanilla, R. (2016) On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law. Math. Meth. Appl. Sci., 39: 4385–4397, which has been published in final form at http://dx.doi.org/10.1002/mma.3867. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving Our aim in this paper is to study generalizations of the nonconserved and conserved Caginalp phase-¿eld systems based on the Maxwell–Cattaneo law with two temperatures for heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. Peer Reviewed Postprint (author's final draft) 2016-10-31 Article Miranville, A., Quintanilla, R. On the Caginalp phase-field systems with two temperatures and the Maxwell–Cattaneo law. "Mathematical methods in the applied sciences", 31 Octubre 2016, vol. 39, núm. 15, p. 4385-4397. 0170-4214 https://hdl.handle.net/2117/90781 10.1002/mma.3867 eng info:eu-repo/grantAgreement/MINECO//MTM2013-42004-P/ES/ANALISIS MATEMATICO DE LAS ECUACIONES EN DERIVADAS PARCIALES DE LA TERMOMECANICA/ Open Access 13 p. application/pdf