Soit la matrice de diffusion, associée à l’équation des ondes dans l’extérieur d’un obstacle non-captif , avec condition de Dirichlet ou Neumann sur . La fonction , dite phase de diffusion, est déterminée par l’égalité . On démontre que admet un développement asymptotique et on calcule les trois premiers coefficients. Notre résultat prouve la conjecture de Majda et Ralston pour des obstacles non-captifs.
Let be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle , with Dirichlet or Neumann boundary conditions on . The function , called scattering phase, is determined from the equality . We show that has an asymptotic expansion as and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.
@article{AIF_1982__32_3_111_0, author = {Petkov, Veselin and Popov, Georgi}, title = {Asymptotic behaviour of the scattering phase for non-trapping obstacles}, journal = {Annales de l'Institut Fourier}, pages = {111--149}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {32}, number = {3}, year = {1982}, doi = {10.5802/aif.882}, mrnumber = {85c:35070}, zbl = {0476.35014}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.882/} }
TY - JOUR AU - Petkov, Veselin AU - Popov, Georgi TI - Asymptotic behaviour of the scattering phase for non-trapping obstacles JO - Annales de l'Institut Fourier PY - 1982 SP - 111 EP - 149 VL - 32 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.882/ DO - 10.5802/aif.882 LA - en ID - AIF_1982__32_3_111_0 ER -
%0 Journal Article %A Petkov, Veselin %A Popov, Georgi %T Asymptotic behaviour of the scattering phase for non-trapping obstacles %J Annales de l'Institut Fourier %D 1982 %P 111-149 %V 32 %N 3 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.882/ %R 10.5802/aif.882 %G en %F AIF_1982__32_3_111_0
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://www.numdam.org/articles/10.5802/aif.882/
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