http://www.cnr.it/ontology/cnr/individuo/prodotto/ID285449
Doubly nonlinear evolution equations as convex minimization (Articolo in rivista)
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- Doubly nonlinear evolution equations as convex minimization (Articolo in rivista) (literal)
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- 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)
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- Akagi G.; Stefanelli U. (literal)
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- http://epubs.siam.org/doi/abs/10.1137/13091909X (literal)
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- 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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