Galerkin approximations for nonlinear evolution inclusions

Shouchuan Hu; Nikolaos S. Papageorgiou

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 4, page 705-720
  • ISSN: 0010-2628

Abstract

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In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.

How to cite

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Hu, Shouchuan, and Papageorgiou, Nikolaos S.. "Galerkin approximations for nonlinear evolution inclusions." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 705-720. <http://eudml.org/doc/247626>.

@article{Hu1994,
abstract = {In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.},
author = {Hu, Shouchuan, Papageorgiou, Nikolaos S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Galerkin approximations; evolution triple; monotone operator; hemicontinuous operator; compact embedding; periodic trajectory; tangent cone; connected set; acyclic set; monotone operator; convergence; Galerkin approximations; nonlinear nonautonomous evolution inclusion; Hilbert space; periodic solutions; multivalued parabolic partial differential equations},
language = {eng},
number = {4},
pages = {705-720},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Galerkin approximations for nonlinear evolution inclusions},
url = {http://eudml.org/doc/247626},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Hu, Shouchuan
AU - Papageorgiou, Nikolaos S.
TI - Galerkin approximations for nonlinear evolution inclusions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 705
EP - 720
AB - In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.ei̇s also worked out in detail.
LA - eng
KW - Galerkin approximations; evolution triple; monotone operator; hemicontinuous operator; compact embedding; periodic trajectory; tangent cone; connected set; acyclic set; monotone operator; convergence; Galerkin approximations; nonlinear nonautonomous evolution inclusion; Hilbert space; periodic solutions; multivalued parabolic partial differential equations
UR - http://eudml.org/doc/247626
ER -

References

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  1. Attouch H., Variational Convergence for Functional and Operator, Pitman, London, 1984. 
  2. DeBlasi F.S., Myjak J., On continuous approximations for multifunctions, Pacific J. Math. 123 (1986), 9-31. (1986) MR0834135
  3. DeBlasi F.S., Myjak J., On the solution sets for differential inclusions, Bulletin Polish Acad. Sci. 33 (1985), 17-23. (1985) MR0798723
  4. Eilenberg S., Montgomery D., Fixed point theorems for multivalued transformations, Amer. J. Math. 68 (1946), 214-222. (1946) Zbl0060.40203MR0016676
  5. Hu S., Papageorgiou N.S., On the topological regularity of the solution set of differential inclusions with state constraints, J. Diff. Equations 107 (1994), in press. (1994) MR1264523
  6. Lakshmikantham V., Leela S., Nonlinear Differential Equations in Abstract Spaces, Pergamon Press, Oxford, 1981. Zbl0456.34002MR0616449
  7. Papageorgiou N.S., Convergence theorems for Banach space valued integrable multifunctions, J. Math. Math. Sci. 10 (1987), 433-442. (1987) Zbl0619.28009MR0896595
  8. Papageorgiou N.S., On infinite dimensional control systems with state and control constraints, Proc. Indian Acad. Sci. 100 (1990), 65-79. (1990) Zbl0703.49018MR1051092
  9. Papageorgiou N.S., A viability result for nonlinear time dependent evolution inclusion, Yokohama Math. Jour. 40 (1992), 73-86. (1992) MR1190002
  10. Papageorgiou N.S., On the bang-bang principle for nonlinear evolution inclusions, Aequationes Math. 45 (1993), 267-280. (1993) Zbl0780.34046MR1212391
  11. Strang G., Fix G., An Analysis of the FInite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973. Zbl0356.65096MR0443377
  12. Zeidler E., Nonlinear Functional Analysis and its Application II, Springer Verlag, New York, 1990. MR0816732

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