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Asymptotic Compactness and Attractors for Phase-Field Equations in ℝ3

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Abstract

In this paper we study the asymptotic behaviour of solutions of the phase-field system on an unbounded domain. We do not assume conditions on the non-linear term ensuring the uniqueness of the Cauchy problem, so that we have to work with multivalued semiflows rather than with semigroups of operators. In this way we prove the existence of a global attractor by considering the convergence in an appropriate weighted space. This result is also new for more restrictive conditions, which guarantee the uniqueness of solutions.

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Authors and Affiliations

  1. Dpto. de Ingeniería Hidráulica y Medio Ambiente, Universidad Politécnica de Valencia, Camino de Vera, s/n 46022, Valencia, Spain

    Francisco Morillas

  2. Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. Universidad, s/n. 03202, Elche (Alicante), Spain

    José Valero

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  1. Francisco Morillas
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  2. José Valero
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Correspondence to José Valero.

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Morillas, F., Valero, J. Asymptotic Compactness and Attractors for Phase-Field Equations in ℝ3 . Set-Valued Anal 16, 861–897 (2008). https://doi.org/10.1007/s11228-008-0096-6

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  • DOI: https://doi.org/10.1007/s11228-008-0096-6

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