no. 2
Decay of solutions of the wave equation in the exterior of several convex bodies
Annales de l'Institut Fourier, Tome 38 (1988) no. 2, pp. 113-146.

On étudie la décroissance des solutions de l’équation des ondes dans l’extérieur de plusieurs objets strictement convexes. Une condition suffisante pour décroissance exponentielle d’énergie locale est exprimée en terme de période et d’application de Poincaré des rayons périodiques dans le domaine extérieur..

We study the decay of solutions to the wave equation in the exterior of several strictly convex bodies. A sufficient condition for exponential decay of the local energy is expressed in terms of the period and the Poincare map of periodic rays in the exterior domain.

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     author = {Ikawa, Mitsuru},
     title = {Decay of solutions of the wave equation in the exterior of several convex bodies},
     journal = {Annales de l'Institut Fourier},
     pages = {113--146},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {38},
     number = {2},
     year = {1988},
     doi = {10.5802/aif.1137},
     mrnumber = {90a:35028},
     zbl = {0636.35045},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1137/}
}
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Ikawa, Mitsuru. Decay of solutions of the wave equation in the exterior of several convex bodies. Annales de l'Institut Fourier, Tome 38 (1988) no. 2, pp. 113-146. doi : 10.5802/aif.1137. http://www.numdam.org/articles/10.5802/aif.1137/

[BGR] C. Bardos, J.-C. Guillot and J. Ralston, La relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application à la théorie de la diffusion, Comm. Partial Diff. Equ., 7 (1982), 905-958. | MR | Zbl

[G] C. Gérard, Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes, Université de Paris-Sud — Département de Mathématiques, 1987.

[I1] M. Ikawa, Decay of solutions of the wave equation in the exterior of two convex obstacles, Osaka J. Math., 19 (1982), 459-509. | MR | Zbl

[I2] M. Ikawa, On the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ., 23 (1983), 127-194. | MR | Zbl

[I3] M. Ikawa, On the poles of the scattering matrix for two convex obstacles, Journées "Équations aux dérivées partielles" de Saint-Jean-de-Monts, 1985. | Numdam | MR | Zbl

[I4] M. Ikawa, Precise informations on the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ., 27 (1987), 69-102. | MR | Zbl

[I5] M. Ikawa, Sur la décroissance d'énergie locale du problème extérieur avec plusieurs (n ≥ 3) obstacles strictement convexes, Séminaire de théorie spectacle et géométrie, 1985-1986. | Numdam | Zbl

[KLS] J. B. Keller, R. M. Lewis and B. D. Seckler, Asymptotic solution of some diffraction problems, Comm. Pure Appl. Math., 9 (1956), 207-265. | MR | Zbl

[LP1] P. D. Lax and R. S. Phillips, Scattering theory, Academic Press, (1967). | Zbl

[LP2] P. D. Lax, R. S. Phillips, A logarithmic bound on the location of the poles of the scattering matrix, Arch. Rat. Mech. and Anal., 40 (1971), 268-280. | MR | Zbl

[Me1] R. Melrose, Singularities and energy decay of acoustical scattering, Duke Math. J., 46 (1979), 43-59. | MR | Zbl

[Me2] R. Melrose, Polynomial bound on the distribution of poles in scattering by an obstacle, Journées "Équations aux dérivées partielles" de Saint-Jean-de-Monts, 1984. | Numdam | Zbl

[MeS] P. Melrose and J. Sjöstrand, Singularities of boundary value problems, I and II, Comm. Pure Appl. Math., 31 (1978), 593-617, 35 (1982), 129-168. | Zbl

[Mi] S. Mizohata, Sur l'analyticité de la fonction spectrale de l'opérateur Δ relatif au problème extérieur, Proc. Japan Acad., 38 (1963), 352-357. | MR | Zbl

[P] V. M. Petkov, La distribution des poles de la matrice de diffusion, Séminaire Goulaouic-Meyer-Schwartz, 1982-1983. | Numdam | Zbl

[R] J. Ralston, Solutions of the wave equation with localized energy, Comm. Pure Appl. Math., 22 (1969), 807-823. | MR | Zbl

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