Weighted Inertia-Dissipation-Energy Functionals for Semilinear Equations

Matthias Liero; Ulisse Stefanelli

Bollettino dell'Unione Matematica Italiana (2013)

  • Volume: 6, Issue: 1, page 1-27
  • ISSN: 0392-4041

Abstract

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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 Γ -convergence and is extended to some time-discrete situation as well.

How to cite

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Liero, Matthias, and Stefanelli, Ulisse. "Weighted Inertia-Dissipation-Energy Functionals for Semilinear Equations." Bollettino dell'Unione Matematica Italiana 6.1 (2013): 1-27. <http://eudml.org/doc/294053>.

@article{Liero2013,
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 $\Gamma$-convergence and is extended to some time-discrete situation as well.},
author = {Liero, Matthias, Stefanelli, Ulisse},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {1-27},
publisher = {Unione Matematica Italiana},
title = {Weighted Inertia-Dissipation-Energy Functionals for Semilinear Equations},
url = {http://eudml.org/doc/294053},
volume = {6},
year = {2013},
}

TY - JOUR
AU - Liero, Matthias
AU - Stefanelli, Ulisse
TI - Weighted Inertia-Dissipation-Energy Functionals for Semilinear Equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/2//
PB - Unione Matematica Italiana
VL - 6
IS - 1
SP - 1
EP - 27
AB - 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 $\Gamma$-convergence and is extended to some time-discrete situation as well.
LA - eng
UR - http://eudml.org/doc/294053
ER -

References

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