| Title:
|
Singular perturbations in optimal control problem with application to nonlinear structural analysis (English) |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
299-320 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper concerns an optimal control problem of elliptic singular perturbations in variational inequalities (with controls appearing in coefficients, right hand sides and convex sets of states as well). The existence of an optimal control is verified. Applications to the optimal control of an elasto-plastic plate with a small rigidity and with an obstacle are presented. For elasto-plastic plates with a moving part of the boundary a primal finite element model is applied and a convergence result is obtained. (English) |
| Keyword:
|
optimal control problem |
| Keyword:
|
singular perturbations in variational inequalities |
| Keyword:
|
convex set |
| Keyword:
|
elasto-plastic plate |
| Keyword:
|
small rigidity |
| Keyword:
|
obstacle |
| MSC:
|
35J85 |
| MSC:
|
49A27 |
| MSC:
|
49A29 |
| MSC:
|
49B34 |
| MSC:
|
49J40 |
| MSC:
|
74K20 |
| idZBL:
|
Zbl 0870.49003 |
| idMR:
|
MR1395688 |
| DOI:
|
10.21136/AM.1996.134328 |
| . |
| Date available:
|
2009-09-22T17:51:51Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134328 |
| . |
| Reference:
|
[1] V. Barbu: Optimal Control of Variational Inequalities. Pitman Advanced Publishing Program, Boston-London.1987. MR 0742624 |
| Reference:
|
[2] H. Brézis et G. Stampacchia: Sur la régularité de la solution d’inéquations elliptiques.Bull. Soc. Math. Franç. 96 (1968), 153–180. MR 0239302 |
| Reference:
|
[3] W. Eckhaus and J.K. Moet: Asymptotic solution in free boundary problems of singularly perturbed elliptic variational inequalities.Differential Equations and Applications, W. Eckhaus and E.M. Jaegar (eds.), North-Holland Publishing Company, Amsterdam, 1978. MR 0516169 |
| Reference:
|
[4] W.M. Greenlee: Singular perturbations of eigenvalues.Arch. Rat. Mech. Anal. 34 (1969), 143–164. MR 0249797, 10.1007/BF00247463 |
| Reference:
|
[5] R. Glowinski: Numerical Methods for Nonlinear Variational Problems.Springer Verlag, New York, 1984. Zbl 0536.65054, MR 0737005 |
| Reference:
|
[6] D. Huet: Singular perturbations of elliptic problems.Annali Math. Pura Appl. 95 (1973), 77–114. Zbl 0279.35010, MR 0328289, 10.1007/BF02410710 |
| Reference:
|
[7] J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design. Theory and application.J. Wiley, New York, 1988. MR 0982710 |
| Reference:
|
[8] C. Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method.Cambridge Univ. Press, Cambridge, 1987. Zbl 0628.65098, MR 0925005 |
| Reference:
|
[9] A. Langenbach: Monotone Potenzial Operatoren in Theorie und Anwendungen.Deutscher V. der Wissenschaften, Berlin, 1976. |
| Reference:
|
[10] J.L. Lions: Pertubations singulières dans les problèmes aux limites et en contrôle optimal. Lect. Notes in Math. 323.Springer Verlag, Berlin, 1973. MR 0600331, 10.1007/BFb0060528 |
| Reference:
|
[11] J.L. Lions: Singular perturbation and singular layers in variational inequalities.Contribution to Nonlinear Analysis, E.H. Zarantonello (ed.), Acad. Press, New York, 1971. MR 0390457 |
| Reference:
|
[12] R. Mignot and J.P. Puel: Optimal control in some variational inequalities.SIAM J. Control Optimiz. 22 (1984), 466–476. MR 0739836, 10.1137/0322028 |
| Reference:
|
[13] U. Mosco: Convergence of convex sets and of solutions of variational inequalities.Advances of Math. 3 (1969), 510–585. Zbl 0192.49101, MR 0298508, 10.1016/0001-8708(69)90009-7 |
| Reference:
|
[14] J.F. Rodrigues: Obstacle Problems in Mathematical Physics.North Holland Math. Studies, Amsterdam, 1986. MR 0880369 |
| . |
