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Weighted Inertia-Dissipation-Energy functionals for semilinear equations (Articolo in rivista)

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Weighted Inertia-Dissipation-Energy functionals for semilinear equations (Articolo in rivista) (literal)

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Matthias Liero, Ulisse Stefanelli (2013)
Weighted Inertia-Dissipation-Energy functionals for semilinear equations
in Bollettino della Unione matematica italiana (2008); Springer International Publishing, CH-6330 Cham (ZG) (Svizzera)
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Weierstrass-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117 Berlin, Germany; Istituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes, CNR, v. Ferrata 1, I-27100 Pavia, Italy (literal)

Titolo

Weighted Inertia-Dissipation-Energy functionals for semilinear equations (literal)

Abstract

We address a global-in-time variational approach to semilinear PDEs of either parabolic or hyperbolic type by means of the so-called Weighted Inertia-Dissipation-Energy (WIDE) functional In particular, minimizers of the WIDE functional are proved to converge, up to subsequences, to weak solutions of the limiting PDE. This entails the possibility of reformulating the limiting differential problem in terms of convex minimization. The WIDE formalism can be used in order to discuss parameters asymptotics via ?-convergence and is extended to some time-discrete situation as well. (literal)

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