On the observability inequalities for exact controllability of wave equations with variable coefficients

SIAM Journal on Control and Optimization

Volumn 37, Issue 5, 1999, Pages 1568-1599

  Yao, Peng Fei ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; GEOMETRICAL OPTICS; GREEN'S FUNCTION; INTEGRATION; OBSERVABILITY; VECTORS; WAVE EQUATIONS;

EXACT CONTROLLABILITY; HESSIAN COMPARISON THEOREM; RIEMANNIAN MANIFOLD;

CONTROLLABILITY;

EID: 0033140929     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012997331482     Document Type: Article

References (20)

1. C. BARDOS, G. LEBEAU, AND J. RAUCH, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), pp. 1024-1065.
2. J. CHEEGER AND D. EBIN, Comparison Theorem in Riemannian Geometry, North-Holland, Amsterdam, 1975.
3. G. CHEN, Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures Appl., 58 (1979), pp. 249-274.
4. ∞ convex functions and manifolds of positive curvature, Acta Math., 137 (1976), pp. 209-245.
5. R. E. GREENE AND H. WU, Function Theory on Manifolds Which Possess a Pole, Lecture Notes in Math. 699, Springer-Verlag, New York, 1979.
6. V. KOMORNIK, Exact Controllability and Stabilization, RAM Res. Appl. Math., Masson/John Wiley, Paris, Chichester, 1994.
7. J. LAGNESE, Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations, 50 (1983), pp. 163-182.
8. J. LAGNESE, The Hilbert uniqueness method: A retrospective, in Optimal Conrol of Partial Differential Equations, Lecture Notes in Control and Inform. Sci. 148, M. Thoma and A. Wyner, eds., Springer-Verlag, New York, 1990, pp. 158-181.
9. I. LASIECKA, J. L. LIONS, AND R. TRIGGIANI, Nonhomogeneous boundary value problems for second-order hyperbolic operators, J. Math. Pures Appl., 65 (1981), pp. 149-192.
10. I. LASIECKA AND R. TRIGGIANI, Exact controllability of the wave equation with Neumann boundary control, Appl. Math. Optim., 19 (1989), pp. 243-290.
11. J. L. LIONS, Contrôlabilité exacte, stabilisation et perturbations des systémes distribués, Vol. 1, Contrôlabilité exacte (E. Zuazua, compiler); Vol. 2, Perturbations; Vol. 3, Stabilisation, Masson, Paris, 1988.
12. J. L. LIONS, Exact controllability, stabilization and perturbations for distributed systems, J. von Neumann Lecture, SIAM Rev., 30 (1988), pp. 1-68.
13. J. RALSTON, Gaussian beams and the propagation of singularities, in Studies in Partial Differential Equations, MAA Stud. Math. 23, W. Littman, ed., Mathematical Association of America, Washington, DC, 1982, pp. 204-248.
14. M. SPIVAK, A Comprehensive Introduction to Differential Geometry II, 2nd ed., Publish or Perish, Berkeley, CA, 1979.
15. D. TATARU, A-priori estimates of Carleman's type in domains with boundary, J. Math. Pures Appl., 73 (1994), pp. 355-387.
16. D. TATARU, Boundary controllability for conservative PDEs, Appl. Math. Optim., 31 (1995), pp. 257-295.
17. D. TATARU, Carleman estimates and unique continuation for solutions to boundary value problems, J. Math. Pures Appl., 75 (1996), pp. 367-408.
18. -1(Ω) of the wave equation with Dirichlet boundary control acting on a portion of the boundary and related problems, Appl. Math. Optim., 18 (1988), pp. 241-277.
19. H. WU, C. L. SHEN, AND Y. L. YU, An Introduction to Riemannian Geometry, University of Beijing, 1989 (in Chinese).
20. P. F. YAO, The observability inequalities for the Euler-Bernoulli equations with variable coefficients in a bounded region, to appear.