Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations (Articolo in rivista)

Type
Label
  • Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations (Articolo in rivista) (literal)
Anno
  • 2006-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1016/j.jde.2006.02.009 (literal)
Alternative label
  • Chill R.; Fiorenza A. (2006)
    Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations
    in Journal of differential equations (Print); Elsevier BV, Amsterdam (Paesi Bassi)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Chill R.; Fiorenza A. (literal)
Pagina inizio
  • 611 (literal)
Pagina fine
  • 632 (literal)
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  • In this paper the rich machinery of the Orlicz space theory, where the study of the role of the growths finds its maximal realization, is fully applied to find convergence and decay estimates of bounded solutions of a quasilinear parabolic equation. It is a relevant example on how different fields (PDEs and Function Space Theory) can meet, to solve a problem of great interest in recent years. (literal)
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  • http://www.elsevier.com/locate/jde (literal)
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  • 228 (literal)
Rivista
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  • 22 (literal)
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  • 2 (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Scopu (literal)
  • Google S (literal)
  • Mathematical Reviews on the web (MathSciNet) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germany Dipartimento di Costruzioni e Metodi Matematici in Architettura, Universitá di Napoli, Via Monteoliveto, 3, I-80134 Napoli, Italy Istituto per le Applicazioni del Calcolo \"Mauro Picone\", Consiglio Nazionale delle Ricerche, via Pietro Castellino, 111, I-80131 Napoli, Italy (literal)
Titolo
  • Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations (literal)
Abstract
  • We study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation ut - div a(x , ? u) + f (x , u) = 0 on a bounded domain, subject to Dirichlet boundary and to initial conditions. The data are supposed to satisfy suitable regularity and growth conditions. Our approach to the convergence result and decay estimate is based on the ?ojasiewicz-Simon gradient inequality which in the case of the semilinear heat equation is known to give optimal decay estimates. The abstract results and their applications are discussed also in the framework of Orlicz-Sobolev spaces. (literal)
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