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A Temperature-Dependent Phase-Field Model for Phase Separation and Damage

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Abstract

In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature concerning phase separation and damage processes in elastic media, in our model we encompass thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More particularly, we prove the existence of “entropic weak solutions”, resorting to a solvability concept first introduced in Feireisl (Comput Math Appl 53:461–490, 2007) in the framework of Fourier–Navier–Stokes systems and then recently employed in Feireisl et al. (Math Methods Appl Sci 32:1345–1369, 2009) and Rocca and Rossi (Math Models Methods Appl Sci 24:1265–1341, 2014) for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117, Berlin, Germany

    Christian Heinemann & Christiane Kraus

  2. Dipartimento di Matematica “F. Casorati”, Università di Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Elisabetta Rocca

  3. DIMI, Università di Brescia, Via Valotti 9, 25133, Brescia, Italy

    Riccarda Rossi

Authors
  1. Christian Heinemann
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  2. Christiane Kraus
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  3. Elisabetta Rocca
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  4. Riccarda Rossi
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Corresponding author

Correspondence to Christian Heinemann.

Additional information

Communicated by G. Dal Maso

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Heinemann, C., Kraus, C., Rocca, E. et al. A Temperature-Dependent Phase-Field Model for Phase Separation and Damage. Arch Rational Mech Anal 225, 177–247 (2017). https://doi.org/10.1007/s00205-017-1102-7

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  • DOI: https://doi.org/10.1007/s00205-017-1102-7

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