A metric approach to a class of doubly nonlinear evolution equations and applications

Riccarda Rossi; Alexander Mielke; Giuseppe Savaré

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 1, page 97-169
  • ISSN: 0391-173X

Abstract

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This paper deals with the analysis of a class of doubly nonlinear evolution equations in the framework of a general metric space. We propose for such equations a suitable metric formulation (which in fact extends the notion of Curve of Maximal Slopefor gradient flows in metric spaces, see [5]), and prove the existence of solutions for the related Cauchy problem by means of an approximation scheme by time discretization. Then, we apply our results to obtain the existence of solutions to abstract doubly nonlinear equations in reflexive Banach spaces. The metric approach is also exploited to analyze a class of evolution equations in L 1 spaces.

How to cite

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Rossi, Riccarda, Mielke, Alexander, and Savaré, Giuseppe. "A metric approach to a class of doubly nonlinear evolution equations and applications." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.1 (2008): 97-169. <http://eudml.org/doc/272287>.

@article{Rossi2008,
abstract = {This paper deals with the analysis of a class of doubly nonlinear evolution equations in the framework of a general metric space. We propose for such equations a suitable metric formulation (which in fact extends the notion of Curve of Maximal Slopefor gradient flows in metric spaces, see [5]), and prove the existence of solutions for the related Cauchy problem by means of an approximation scheme by time discretization. Then, we apply our results to obtain the existence of solutions to abstract doubly nonlinear equations in reflexive Banach spaces. The metric approach is also exploited to analyze a class of evolution equations in $L^1$ spaces.},
author = {Rossi, Riccarda, Mielke, Alexander, Savaré, Giuseppe},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {existence; approximation result; Cauchy problem; superlinear dissipation functional; time discretization},
language = {eng},
number = {1},
pages = {97-169},
publisher = {Scuola Normale Superiore, Pisa},
title = {A metric approach to a class of doubly nonlinear evolution equations and applications},
url = {http://eudml.org/doc/272287},
volume = {7},
year = {2008},
}

TY - JOUR
AU - Rossi, Riccarda
AU - Mielke, Alexander
AU - Savaré, Giuseppe
TI - A metric approach to a class of doubly nonlinear evolution equations and applications
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2008
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 1
SP - 97
EP - 169
AB - This paper deals with the analysis of a class of doubly nonlinear evolution equations in the framework of a general metric space. We propose for such equations a suitable metric formulation (which in fact extends the notion of Curve of Maximal Slopefor gradient flows in metric spaces, see [5]), and prove the existence of solutions for the related Cauchy problem by means of an approximation scheme by time discretization. Then, we apply our results to obtain the existence of solutions to abstract doubly nonlinear equations in reflexive Banach spaces. The metric approach is also exploited to analyze a class of evolution equations in $L^1$ spaces.
LA - eng
KW - existence; approximation result; Cauchy problem; superlinear dissipation functional; time discretization
UR - http://eudml.org/doc/272287
ER -

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