Set-Valued Analysis

, 16:861 | Cite as

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.

Keywords

Setvalued dynamical system Global attractor Phase-field equations Unbounded domain 

Mathematics Subject Classifications (2000)

35B40 35B41 35K55 35K57 37B25 58C06 
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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Dpto. de Ingeniería Hidráulica y Medio AmbienteUniversidad Politécnica de ValenciaValenciaSpain
  2. 2.Centro de Investigación OperativaUniversidad Miguel HernándezElche (Alicante)Spain

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