| Title:
|
Galerkin approximations for nonlinear evolution inclusions (English) |
| Author:
|
Hu, Shouchuan |
| Author:
|
Papageorgiou, Nikolaos S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
705-720 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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.e\. is also worked out in detail. (English) |
| Keyword:
|
Galerkin approximations |
| Keyword:
|
evolution triple |
| Keyword:
|
monotone operator |
| Keyword:
|
hemicontinuous operator |
| Keyword:
|
compact embedding |
| Keyword:
|
periodic trajectory |
| Keyword:
|
tangent cone |
| Keyword:
|
connected set |
| Keyword:
|
acyclic set |
| MSC:
|
34A45 |
| MSC:
|
34A60 |
| MSC:
|
34G20 |
| MSC:
|
34G99 |
| MSC:
|
35B10 |
| MSC:
|
35G10 |
| MSC:
|
35K22 |
| MSC:
|
35K25 |
| MSC:
|
35R70 |
| idZBL:
|
Zbl 0819.34011 |
| idMR:
|
MR1321241 |
| . |
| Date available:
|
2009-01-08T18:14:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118712 |
| . |
| Reference:
|
[1] Attouch H.: Variational Convergence for Functional and Operator.Pitman, London, 1984. |
| Reference:
|
[2] DeBlasi F.S., Myjak J.: On continuous approximations for multifunctions.Pacific J. Math. 123 (1986), 9-31. MR 0834135 |
| Reference:
|
[3] DeBlasi F.S., Myjak J.: On the solution sets for differential inclusions.Bulletin Polish Acad. Sci. 33 (1985), 17-23. MR 0798723 |
| Reference:
|
[4] Eilenberg S., Montgomery D.: Fixed point theorems for multivalued transformations.Amer. J. Math. 68 (1946), 214-222. Zbl 0060.40203, MR 0016676 |
| Reference:
|
[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. MR 1264523 |
| Reference:
|
[6] Lakshmikantham V., Leela S.: Nonlinear Differential Equations in Abstract Spaces.Pergamon Press, Oxford, 1981. Zbl 0456.34002, MR 0616449 |
| Reference:
|
[7] Papageorgiou N.S.: Convergence theorems for Banach space valued integrable multifunctions.J. Math. Math. Sci. 10 (1987), 433-442. Zbl 0619.28009, MR 0896595 |
| Reference:
|
[8] Papageorgiou N.S.: On infinite dimensional control systems with state and control constraints.Proc. Indian Acad. Sci. 100 (1990), 65-79. Zbl 0703.49018, MR 1051092 |
| Reference:
|
[9] Papageorgiou N.S.: A viability result for nonlinear time dependent evolution inclusion.Yokohama Math. Jour. 40 (1992), 73-86. MR 1190002 |
| Reference:
|
[10] Papageorgiou N.S.: On the bang-bang principle for nonlinear evolution inclusions.Aequationes Math. 45 (1993), 267-280. Zbl 0780.34046, MR 1212391 |
| Reference:
|
[11] Strang G., Fix G.: An Analysis of the FInite Element Method.Prentice-Hall, Englewood Cliffs, NJ, 1973. Zbl 0356.65096, MR 0443377 |
| Reference:
|
[12] Zeidler E.: Nonlinear Functional Analysis and its Application II.Springer Verlag, New York, 1990. MR 0816732 |
| . |
