Asymptotic expansion and convergence theorem of control and observation on the boundary for second-order elliptic equation with highly oscillatory coefficients

Mathematical Models and Methods in Applied Sciences

Volumn 14, Issue 3, 2004, Pages 417-437

  Cao, Li Qun ^a  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Asymptotic expansion; Homogenization; Optimal control

Indexed keywords

EID: 7244219756     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202504003295     Document Type: Article

References (18)

1. R. A. Adams, Sobolev Spaces (Academic Press, 1975).
2. A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures (North-Holland, 1978).
3. L. Q. Cao, J. Z. Cui and D. C. Zhu, Multiscale asymptotic analysis and numerical simulation for the second-order Helmholtz with rapidly oscillating coefficients over general convex domains, SIAM Numer. Anal. 40 (2003) 543-577.
4. L. Q. Cao and J. Z. Cui, Asymptotic expansions and numerical algorithms of eigenvalues and eigenfunctions of the Dirichlet problem for second order elliptic equations in perforated domains, Numer. Math. 96 (2004) 525-581.
5. C. Conca, A. Osses and J. Saint Jean Paulin, A semilinear control problem involving homogenization, Electron. J. Diff. Eqns. 06 (2001) 109-122.
6. P. Donato and A. Nabil, Homogénéisation et contrôlabitité approchée de l'équation de la chaleur dans domaines perforés, C.R.A.S. 324 (1997) 789-794.
7. C. Fabre, J. P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation, Proc. Roy. Soc. Edinburgh A125 (1995) 31-61.
8. P. Grisvard, Behavior of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain, in Numerical Solution of Partial Differential Equations III, eds. B. Hubbard (Academic Press, 1976), pp. 207-274.
9. T. Y. Hou, X. H. Wu and Z. Cai, Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients, Math. Comp. 68 (1999) 913-943.
10. S. Kesavan and S. Jean Paulin, Homogenization of an optimal control problem, SIAM J. Control Optim. 35 (1997) 1557-1573.
11. S. Kesavan and S. Jean Paulin, Optimal control on perforated domains, J. Math. Anal. Appl. 229 (1999) 563-586.
12. J. L. Lions, Remarks on the theory of optimal control of distributed systems, in Control Theory of Systems Governed by Partial Differential Equations, eds. A. K. Aziz et al. (Academic Press, 1977), pp. 1-103.
13. J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations (Springer-Verlag, 1970).
14. J. L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev. 30 (1988) 1-68.
15. J. L. Lions, Some Methods in the Mathematical Analysis of Systems and Their Control (Science Press, 1981).
16. J. L. Lions, Some Aspects of the Optimal Control of Distributed Parameter Systems (SIAM, 1972).
17. O. A. Oleinik, A. S. Shamaev and G. A. Yosifian, Mathematical Problems in Elasticity and Homogenization (North-Holland, 1992).
18. A. Osses and J. P. Fuel, On the controllability of the Laplace equation observed on an interior curve, Rev. Mat. Complut. 11 (1998) 403-441.