Geodesic
Optimal control of variational inequality with applications to axisymmetric shells
Applications of Mathematics, Tome 32 (1987) no. 6, pp. 459-479
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.
The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.
DOI : 10.21136/AM.1987.104277
Classification : 49A27, 49A29, 58E25, 58E35, 58E99, 74K15, 74P99
Keywords: second invariant of the stress deviator; smooth regularized control problems; optimal shape design; axisymmetric shells; elliptic, linear symmetric operator; first order necessary conditions of optimality; nonsmooth; nonconvex infinite dimensional opimization problem 
@article{10_21136_AM_1987_104277,
     author = {Lov{\'\i}\v{s}ek, J\'an},
     title = {Optimal control of variational inequality with applications to axisymmetric shells},
     journal = {Applications of Mathematics},
     pages = {459--479},
     year = {1987},
     volume = {32},
     number = {6},
     doi = {10.21136/AM.1987.104277},
     mrnumber = {0916062},
     zbl = {0647.73042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104277/}
}
TY  - JOUR
AU  - Lovíšek, Ján
TI  - Optimal control of variational inequality with applications to axisymmetric shells
JO  - Applications of Mathematics
PY  - 1987
SP  - 459
EP  - 479
VL  - 32
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104277/
DO  - 10.21136/AM.1987.104277
LA  - en
ID  - 10_21136_AM_1987_104277
ER  - 
%0 Journal Article
%A Lovíšek, Ján
%T Optimal control of variational inequality with applications to axisymmetric shells
%J Applications of Mathematics
%D 1987
%P 459-479
%V 32
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104277/
%R 10.21136/AM.1987.104277
%G en
%F 10_21136_AM_1987_104277
Lovíšek, Ján. Optimal control of variational inequality with applications to axisymmetric shells. Applications of Mathematics, Tome 32 (1987) no. 6, pp. 459-479. doi: 10.21136/AM.1987.104277

[1] R. A. Adams: Sobolev spaces. Academic Press, New York, San Francisco, London 1975. | MR | Zbl

[2] H. Attouch: Convergence des solutions d'inequations variationnelles avec obstacle. Proceedings of the international meeting on recent methods in nonlinear analysis. Rome, may 1978, ed. by E. De Giorgi - E. Magenes - U. Mosco.

[3] V. Barbu: Optimal control of variational inequalities. Pitman Advanced Publishing Program, Boston, London, Melbourne 1984. | MR | Zbl

[4] I. Boccardo A. Dolcetta: Stabilita delle soluzioni di disequazioni variazionali ellitiche e paraboliche quasi - lineari. Ann. Universeta Ferrara, 24 (1978), 99-111.

[5] J. M. Boisserie, Glowinski: Optimization of the thickness law for thin axisymmetric shells. Computers 8. Structures, 8 (1978), 331-343. | Zbl

[6] I. Hlaváček: Optimalization of the shape of axisymmetric shells. Aplikace matematiky 28, с. 4, pp. 269-294. | MR

[7] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod Paris, 1969. | MR | Zbl

[8] F. Mignot: Controle dans les inéquations variationelles elliptiques. Journal Functional Analysis. 22 (1976), 130-185. | DOI | MR | Zbl

[9] J. Nečas: Les méthodes directes en theorie des équations elliptiques. Academia, Praha, 1967. | MR

[10] J. Nečas I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies. An introduction. Amsterdam, Elsevier, 1981. | MR

[11] P. D. Panagiotopoulos: Inequality problems in mechanics and applications. Birkhäuser, Boston-Basel-Stuttgart, 1985. | MR | Zbl

[12] J. P. Yvon: Controle optimal de systémes gouvernes par des inéquations variationnelles. Rapport Laboria, February 1974.

[13] O. C. Zienkiewcz: The Finite Element Method in Engineering. Science, McGraw Hill, London, 1984.

Cité par Sources :