Asymptotic behaviour of the scattering phase for non-trapping obstacles
Annales de l'Institut Fourier, Tome 32 (1982) no. 3, pp. 111-149.

Soit S(λ) la matrice de diffusion, associée à l’équation des ondes dans l’extérieur d’un obstacle non-captif 𝒪R n , n3 avec condition de Dirichlet ou Neumann sur 𝒪. La fonction s(λ), dite phase de diffusion, est déterminée par l’égalité e -2πis(λ) = det S(λ). On démontre que s(λ) admet un développement asymptotique s(λ) j=0 c j λ n-j et on calcule les trois premiers coefficients. Notre résultat prouve la conjecture de Majda et Ralston pour des obstacles non-captifs.

Let S(λ) be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle 𝒪R n , n3 with Dirichlet or Neumann boundary conditions on 𝒪. The function s(λ), called scattering phase, is determined from the equality e -2πis(λ) = det S(λ). We show that s(λ) has an asymptotic expansion s(λ) j=0 c j λ n-j as λ+ and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.

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Petkov, Veselin; Popov, Georgi. Asymptotic behaviour of the scattering phase for non-trapping obstacles. Annales de l'Institut Fourier, Tome 32 (1982) no. 3, pp. 111-149. doi : 10.5802/aif.882. http://archive.numdam.org/articles/10.5802/aif.882/

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