Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

Stanisław Migórski

Open Mathematics (2012)

  • Volume: 10, Issue: 6, page 1953-1968
  • ISSN: 2391-5455

Abstract

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We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.

How to cite

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Stanisław Migórski. "Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems." Open Mathematics 10.6 (2012): 1953-1968. <http://eudml.org/doc/269110>.

@article{StanisławMigórski2012,
abstract = {We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.},
author = {Stanisław Migórski},
journal = {Open Mathematics},
keywords = {Hemivariational inequality; Subdifferential; Quasi-static; Multifunction; Nonconvex; Viscoelasticity; hemivariational inequality; subdifferential; quasi-static; multifunction; nonconvex; viscoelasticity},
language = {eng},
number = {6},
pages = {1953-1968},
title = {Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems},
url = {http://eudml.org/doc/269110},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Stanisław Migórski
TI - Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 1953
EP - 1968
AB - We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.
LA - eng
KW - Hemivariational inequality; Subdifferential; Quasi-static; Multifunction; Nonconvex; Viscoelasticity; hemivariational inequality; subdifferential; quasi-static; multifunction; nonconvex; viscoelasticity
UR - http://eudml.org/doc/269110
ER -

References

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