Suboptimal boundary controls for elliptic equation in critically perforated domain

D'Apice, Ciro; De Maio, Umberto; Kogut, Peter I.

doi:10.1016/j.anihpc.2007.07.001

D'Apice, Ciro ; De Maio, Umberto ; Kogut, Peter I.

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 6, pp. 1073-1101.

MR Zbl

DOI : 10.1016/j.anihpc.2007.07.001

@article{AIHPC_2008__25_6_1073_0,
     author = {D'Apice, Ciro and De Maio, Umberto and Kogut, Peter I.},
     title = {Suboptimal boundary controls for elliptic equation in critically perforated domain},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1073--1101},
     publisher = {Elsevier},
     volume = {25},
     number = {6},
     year = {2008},
     doi = {10.1016/j.anihpc.2007.07.001},
     mrnumber = {2466322},
     zbl = {1170.35015},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2007.07.001/}
}

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D'Apice, Ciro; De Maio, Umberto; Kogut, Peter I. Suboptimal boundary controls for elliptic equation in critically perforated domain. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 6, pp. 1073-1101. doi : 10.1016/j.anihpc.2007.07.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2007.07.001/

Bibliographie
Cité par

[1] Bouchitté G., Fragala I., Homogenization of thin structures by two-scale method with respect to measures, SIAM J. Math. Anal. 32 (6) (2001) 1198-1226. | MR | Zbl

[2] G. Buttazzo, Γ-convergence and its applications to some problem in the calculus of variations, in: School on Homogenization, ICTP, Trieste, September 6-17, 1993, 1994, pp. 38-61.

[3] Buttazzo G., Dal Maso G., Γ-convergence and optimal control problems, J. Optim. Theory Appl. 32 (1982) 385-407. | MR | Zbl

[4] Carbone L., De Arcangelis R., Unbounded Functionals in the Calculus of Variations. Representation, Relaxation, and Homogenization, Chapman and Hall/CRC, New York, 2002. | MR | Zbl

[5] Cardone G., D'Apice C., De Maio U., Homogenization in perforated domains with mixed conditions, Nonlinear Diff. Equ. Appl. 9 (2002) 246-325. | MR | Zbl

[6] Casado-Díaz J., Existence of a sequence satisfying Cioranescu-Murat conditions in homogenization of Dirichlet problems in perforated domains, Rend. Mat. Appl. (7) 16 (1996) 387-413. | MR | Zbl

[7] Cioranescu D., Donato P., Murat F., Zuazua E., Homogenization and correctors for the wave equation in domains with small holes, Ann. Sc. Norm. Super. Pisa, Sc. Fis. Mat. 17 (4) (1991) 251-293. | Numdam | MR | Zbl

[8] Cioranescu D., Donato P., Zuazua E., Exact boundary controllability for the wave equation in domains with small holes, J. Math. Pures Appl. 71 (1992) 343-377. | MR | Zbl

[9] Cioranescu D., Murat F., Un terme étrage venu d'ailleurs, in: Nonlinear Partial Differential Equations and their applications. Collége de France Seminar, Research Notes in Mathematics, Pitman, London, 1981, vol. II, pp. 58-138, vol. III, pp. 157-178. | Zbl

[10] Cioranescu D., Saint Jean Paulin J., Homogenization in open sets with holes, J. Math. Anal. Appl. 71 (1978) 590-607. | MR | Zbl

[11] Conca C., Donato P., Nonhomogeneous Neumann problems in domains with small holes, Modélisation Mathématique et Analyse Numérique 22 (4) (1988) 561-608. | Numdam | MR | Zbl

[12] Corbo Esposito A., D'Apice C., Gaudiello A., A homogenization problem in a perforated domain with both Dirichlet and Neumann conditions on the boundary of the holes, Asymptodic Anal. 31 (2002) 297-316. | MR | Zbl

[13] Coron J.-M., Crépeau E., Exact boundary controllability of a nonlinear KdV equation with critical length, J. Eur. Math. Soc. (JEMS) 6 (3) (2004) 367-398. | MR | Zbl

[14] Dal Maso G., Murat F., Asymptotic behaviour and correctors for Dirichlet problem in perforated domains with homogeneous monotone operators, Ann. Sc. Norm. Sup. Pisa Cl. Sci. 24 (4) (1997) 239-290. | Numdam | MR | Zbl

[15] Evans L.C., Gariepy R.F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, FL, 1992. | MR | Zbl

[16] Fursikov A.V., Optimal Control of Distributed Systems. Theory and Applications, Amer. Math. Soc., 2000. | MR | Zbl

[17] Ioffe A.D., Tikhomirov V.M., Theory of Extremal Problems, Nauka, Moskow, 1974, (in Russian). | MR

[18] Kesavan S., Saint Jean Paulin J., Optimal control on perforated domains, J. Math. Anal. Appl. 229 (1999) 563-586. | MR | Zbl

[19] Kogut P.I., S-convergence in homogenization theory of optimal control problems, Ukrain. Mat. Zh. 49 (11) (1997) 1488-1498, (in Russian); English transl. in:, Ukrainian Math. J. 49 (11) (1997) 1671-1682. | MR | Zbl

[20] Kogut P.I., Leugering G., On S-homogenization of an optimal control problem with control and state constraints, J. Anal. Appl. 20 (2) (2001) 395-429. | MR | Zbl

[21] Lions J.L., Équations différentielles opérationnelles, Springer-Verlag, Berlin, 1961. | MR | Zbl

[22] Lions J.L., Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, 1971. | MR | Zbl

[23] Marchenko V.A., Khruslov E.Ya., Boundary Value Problems in Domain with Fine-Grained Boundary, Naukova Dumka, Kyiv, 1974. | Zbl

[24] Nandakumar A.K., Convergence of the boundary control for the wave equation in domains with holes of critical size, Electron. J. Differential Equations 2002 (35) (2002) 1-10. | MR | Zbl

[25] Pastukhova S.E., On the convergence of hyperbolic semigroups in variable Hilbert spaces, J. Math. Sci. 127 (5) (2005) 2263-2283. | MR | Zbl

[26] Saint Jean Paulin J., Zoubairi H., Optimal control and “strange term” for the Stokes problem in perforated domains, Portugal. Math. 59 (2) (2002) 161-178. | MR | Zbl

[27] Scrypnik I.V., Averaging nonlinear Dirichlet problems in domains with channels, Soviet Math. Dokl. 42 (1991) 853-857. | MR | Zbl

[28] Zhikov V.V., On an extension of the method of two-scale convergence and its applications, Sbornik Math. 191 (7) (2000) 973-1014. | MR | Zbl

[29] Zhikov V.V., Kozlov S.M., A Oleinik O., Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994. | MR | Zbl

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