Spectral sequences for quadratic pencils and the inverse spectral problem for the damped wave equation

Journal des Mathematiques Pures et Appliquees

Volumn 78, Issue 9, 1999, Pages 965-980

  Freitas, Pedro ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Damped wave equation; Hermitian pencils; Weyl's inequalities

Indexed keywords

EID: 0033539420     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(99)00135-X     Document Type: Article

References (23)

1. Y. Colin De Verdière, Construction de laplaciens dont une partie finie du spectre est donnée, Ann. Sci. École Norm. Sup. 20 (1987) 599-615.
2. Y. Colin De Verdière, Multiplicities of eigenvalues and tree-width of graphs, J. Comb. Theory B 74 (1998) 121-146.
3. S. Cox and E. Zuazua, The rate at which energy decays in a damped string, Comm. Partial Differential Equations 19 (1994) 213-243.
4. P. Freitas, On some eigenvalue problems related to the wave equation with indefinite damping, J. Differential Equations 127 (1996) 320-335.
5. P. Freitas, Optimizing the rate of decay of solutions of the wave equation using genetic algorithms: A counterexample to the constant damping conjecture, SIAM J. Control Optim. 39 (1999) 376-387.
6. P. Freitas, M. Grinfeld and P.A. Knight, Stability for finite-dimensional systems with indefinite damping, Adv. Math. Sci. Appl. 1 (1997) 435-446.
7. P. Freitas and P. Lancaster, On the optimal value of the spectral abscissa for a system of linear oscillators, SIAM J. Matrix Anal. Appl., to appear.
8. P. Freitas and E. Zuazua, Stability results for the wave equation with indefinite damping, J. Differential Equations 132 (1996) 338-352.
9. I. Gohberg, P. Lancaster and L. Rodman, Matrix Polynomials, Academic Press, New York, 1982.
10. I. Gohberg, P. Lancaster and L. Rodman, Quadratic matrix polynomials with a parameter, Adv. Appl. Math. 7 (1986) 253-281.
11. A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954) 4-7.
12. A. Horn and C.A. Johnson, Matrix Analysis, Cambridge Univ. Press, Cambridge, 1985.
13. A. Horn and C.A. Johnson, Topics in Matrix Analysis, Cambridge Univ. Press, Cambridge, 1995.
14. T. Kato, Perturbation Theory of Linear Operators, Springer, New York, 1980.
15. M.A. Krasnosel'skii, G.M. Vainikko, P.P. Zabreiko, Ya.B. Rutitskii and V.Ya. Stetsenko, Approximate Solution of Operator Equations, Wolters-Noordhoff Publishing, Groningen, 1972.
16. H.J. Landau, The inverse eigenvalue problem for real symmetric toplitz matrices, J. Amer. Math. Soc. 7 (1994) 749-767.
17. G. Lebeau, Équation des ondes amorties, in: Algebraic and Geometric Methods in Mathematical Physics (Kaciveli, 1993), Math. Phys. Stud. 19, Kluwer Acad. Publ, Dordrecht, 1996, pp. 73-109.
18. S. Levendorskiǐ, Asymptotic Distribution of Eigenvalues of Differential Operators (translated from the Russian), Mathematics and its Applications (Soviet Series) 53, Kluwer Acad. Publ., Dordrecht, 1990.
19. M. Marden, Geometry of Polynomials, Mathematical Survays and Monographs, Vol. 3, Amer. Math. Soc., 1989.
20. L. Mirsky, Matrices with prescribed characteristic roots and diagonal elements, J. London Math. Soc. 33 (1958) 14-21.
21. J. Pöschel and E. Trubowitz, Inverse Spectral Theory, Pure and Applied Mathematics, Vol. 130, Academic Press, London, 1987.
22. A. Sourour, A factorization theorem for matrices, Linear and Multilinear Algebra 19 (1986) 141-147.
23. H. Weyl, Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. U.S.A. 35 (1949) 408-411.