Doubly nonlinear evolution equations as convex minimization (Articolo in rivista)

Type
Label
  • Doubly nonlinear evolution equations as convex minimization (Articolo in rivista) (literal)
Anno
  • 2014-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1137/13091909X (literal)
Alternative label
  • Akagi G.; Stefanelli U. (2014)
    Doubly nonlinear evolution equations as convex minimization
    in SIAM Journal on Mathematical Analysis; Society for Industrial and Applied Mathematics, Philadelphia, PA (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Akagi G.; Stefanelli U. (literal)
Pagina inizio
  • 1922 (literal)
Pagina fine
  • 1945 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://epubs.siam.org/doi/abs/10.1137/13091909X (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 46 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 3 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Graduate School of System Informatics, Kobe University, Kobe, Japan; Istituto di Matematica Applicata e Tecnologie Informatiche \"E. Magenes\" - CNR, Pavia, Italy (literal)
Titolo
  • Doubly nonlinear evolution equations as convex minimization (literal)
Abstract
  • We present a variational reformulation of a class of doubly nonlinear parabolic equations as (limits of) constrained convex minimization problems. In particular, an $\varepsilon$-dependent family of weighted energy-dissipation (WED) functionals on entire trajectories is introduced and proved to admit minimizers. These minimizers converge to solutions of the original doubly nonlinear equation as $\varepsilon \to 0$. The argument relies on the suitable dualization of the former analysis of [G. Akagi and U. Stefanelli, J. Funct. Anal., 260 (2011), pp. 2541--2578] and results in a considerable extension of the possible application range of the WED functional approach to nonlinear diffusion phenomena, including the Stefan problem and the porous media equation. (literal)
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