Ikawa, Mitsuru Decay of solutions of the wave equation in the exterior of several convex bodies. (English) Zbl 0636.35045 Ann. Inst. Fourier 38, No. 2, 113-146 (1988). 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 Poincaré map of periodic rays in the exterior domain. Reviewer: M.Ikawa Cited in 1 ReviewCited in 68 Documents MSC: 35L05 Wave equation 35B40 Asymptotic behavior of solutions to PDEs Keywords:exterior of several strictly convex bodies; exponential decay; local energy; Poincaré map; periodic rays × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [BGR] , and , 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. · Zbl 0496.35067 [2] [G] , Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes, Université de Paris-Sud — Département de Mathématiques, 1987. [3] [I1] , Decay of solutions of the wave equation in the exterior of two convex obstacles, Osaka J. Math., 19 (1982), 459-509. · Zbl 0498.35008 [4] [I2] , On the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ., 23 (1983), 127-194. · Zbl 0561.35060 [5] [I3] , On the poles of the scattering matrix for two convex obstacles, Journées “Équations aux dérivées partielles” de Saint-Jean-de-Monts, 1985. · Zbl 0587.35057 [6] [I4] , Precise informations on the poles of the scattering matrix for two strictly convex obstacles, J. Math. Kyoto Univ., 27 (1987), 69-102. · Zbl 0637.35068 [7] [I5] , Sur la décroissance d’énergie locale du problème extérieur avec plusieurs (n ≥ 3) obstacles strictement convexes, Séminaire de théorie spectacle et géométrie, 1985-1986. · Zbl 0900.35098 [8] [KLS] , and , Asymptotic solution of some diffraction problems, Comm. Pure Appl. Math., 9 (1956), 207-265. · Zbl 0073.44105 [9] [LP1] and , Scattering theory, Academic Press, (1967). · Zbl 0186.16301 [10] [LP2] , , A logarithmic bound on the location of the poles of the scattering matrix, Arch. Rat. Mech. and Anal., 40 (1971), 268-280. · Zbl 0216.13002 [11] [Me1] , Singularities and energy decay of acoustical scattering, Duke Math. J., 46 (1979), 43-59. · Zbl 0415.35050 [12] [Me2] , Polynomial bound on the distribution of poles in scattering by an obstacle, Journées “Équations aux dérivées partielles” de Saint-Jean-de-Monts, 1984. · Zbl 0621.35073 [13] [MeS] and , Singularities of boundary value problems, I and II, Comm. Pure Appl. Math., 31 (1978), 593-617, 35 (1982), 129-168. · Zbl 0546.35083 [14] [Mi] , Sur l’analyticité de la fonction spectrale de l’opérateur Δ relatif au problème extérieur, Proc. Japan Acad., 38 (1963), 352-357. · Zbl 0122.33802 [15] [P] , La distribution des poles de la matrice de diffusion, Séminaire Goulaouic-Meyer-Schwartz, 1982-1983. · Zbl 0537.35061 [16] [R] , Solutions of the wave equation with localized energy, Comm. Pure Appl. Math., 22 (1969), 807-823. · Zbl 0209.40402 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.