This is a preview of subscription content, log in via an institution to check access.
Bibliographie
[FL]Fernandez, C. &Lavine, R., Lower bounds for resonance width in potential and obstacle scattering.Comm. Math. Phys., 128 (1990), 263–284.
[G]Gérard, C., Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes.Mém. Soc. Math. France (N.S.), 31 (1988), 1–146.
[I1]Ikawa M., Decay of solutions of the wave equation in the exterior of several convex bodies.Ann. Inst. Fourier (Grenoble) 38 (1988), 113–146.
[I2] — Decay of solutions of the wave equation in the exterior of two convex bodies.Osaka J. Math. 19 (1982), 459–509.
[I3] —, Trapping obstacles, with a sequence of poles converging to the real axis.Osaka J. Math., 22 (1985), 657–689.
[I4] —, On the poles of the scattering matrix for two strictly convex obstacles.J. Math. Kyoto Univ., 23 (1983), 127–194.
[Le]Lebeau, G., Equation des ondes amorties, dansAlgebraic and Geometric Methods in Mathematical Physics (Kaciveli, 1993), pp. 73–109. Kluwer Acad. Publ., Dordrecht, 1996.
[LP1]Lax, P. D., &Phillips, R. S., The acoustic equation with an indefinite energy form and the Schrödinger equation.J. Funct. Anal. 1 (1967), 37–83.
[LP2] —Scattering Theory, 2e édition. Pure Appl. Math., 26. Academic Press, Boston, MA, 1989.
[LR1]Lebeau, G. &Robbiano, L., Contrôle exact de l'équation de la chaleur.Comm. Partial Differential Equations, 20 (1995), 335–356.
[LR2]Lebeau, G. & Robbiano, L., Stabilisation de l'équation des ondes, par le bord. Prépublication de l'université de Paris-Sud 95-40, 1995.
[Mi]Milnor, J.,Lectures on the h-Cobordism Theorem, Princeton Univ. Press, Princeton, NJ, 1965.
[Mo1]Morawetz, C. S., The decay of solutions of the exterior initial-boundary value problem for the wave equation.Comm. Pure Appl. Math., 14 (1961), 561–568.
[Mo2] —, Decay of solutions of the exterior problem for the wave equation.Comm. Pure Appl. Math., 28 (1975), 229–264.
[MS]Melrose, R. B. &Sjöstrand, J., Singularities of boundary value problems I.Comm. Pure Appl. Math., 31 (1978), 593–617.
[N]Nédélec, J. C., Quelques propriétés, logarithmiques des fonctions, de Hankel.C. R. Acad. Sci. Paris Sér. I. Math., 314 (1992), 507–510.
[Ra1]Ralston, J. V., Solutions of the wave equation with localized energy.Comm. Pure Appl. Math. 22 (1969), 807–823.
[Ra2] —, Trapped rays in spherically symmetric media and poles of the scattering matrix.Comm. Pure Appl. Math., 24 (1971), 571–582.
[RS]Reed, M. &Simon, B.,Methods of Modern Mathematical Physics, Volumes I–IV. Academic Press, New York-London, 1972–1979.
[Va]Vainberg, B. R.,Asymptotic Methods in Equations of Mathematical Physics, Gordon & Breach, New York, 1989.
[Vo]Vodev, G., Sharp bounds on the number of scattering poles in even-dimensional spaces.Duke Math. J., 74 (1994), 1–17.
[Wal]Walker, H. F., Some remarks on the local energy decay of solutions of the initialboundary value problem for the wave equation in unbounded domains.J. Differential Equations, 23 (1977), 459–471.
[Wat]Watson, G. N.,A Treatise on the Theory of Bessel Functions, 2e édition. Cambridge Univ. Press, Cambridge, 1944.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Burq, N. Décroissance de l'énergie locale de l'équation des ondes pour le problème extérieur et absence de résonance au voisinage du réel. Acta Math. 180, 1–29 (1998). https://doi.org/10.1007/BF02392877
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02392877