Parametrized relaxation for evolution inclusions of the subdifferential type

Nikolaos S. Papageorgiou

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 1, page 9-28
  • ISSN: 0044-8753

Abstract

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In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdifferentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the “Filippov-Gronwall” inequality and using it, we prove the parametric relaxation theorem. An example of a parabolic distributed parameter system is also worked out in detail.

How to cite

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Papageorgiou, Nikolaos S.. "Parametrized relaxation for evolution inclusions of the subdifferential type." Archivum Mathematicum 031.1 (1995): 9-28. <http://eudml.org/doc/247698>.

@article{Papageorgiou1995,
abstract = {In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdifferentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the “Filippov-Gronwall” inequality and using it, we prove the parametric relaxation theorem. An example of a parabolic distributed parameter system is also worked out in detail.},
author = {Papageorgiou, Nikolaos S.},
journal = {Archivum Mathematicum},
keywords = {subdifferential; relaxation theorem; Filippov-Gronwall inequality; lower semicontinuous multifunction; continuous selector; weak norm; Filippov-Gronwall estimate; nonlinear evolution inclusions of the subdifferential type; continuous dependence; parametric relaxation theorem; parabolic distributed parameter system},
language = {eng},
number = {1},
pages = {9-28},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Parametrized relaxation for evolution inclusions of the subdifferential type},
url = {http://eudml.org/doc/247698},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
TI - Parametrized relaxation for evolution inclusions of the subdifferential type
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 1
SP - 9
EP - 28
AB - In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdifferentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the “Filippov-Gronwall” inequality and using it, we prove the parametric relaxation theorem. An example of a parabolic distributed parameter system is also worked out in detail.
LA - eng
KW - subdifferential; relaxation theorem; Filippov-Gronwall inequality; lower semicontinuous multifunction; continuous selector; weak norm; Filippov-Gronwall estimate; nonlinear evolution inclusions of the subdifferential type; continuous dependence; parametric relaxation theorem; parabolic distributed parameter system
UR - http://eudml.org/doc/247698
ER -

References

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