Geodesic
Asymptotics of the scattering operator for the wave equation in a~singularly perturbed domain
Sbornik. Mathematics, Tome 212 (2021) no. 10, pp. 1436-1470

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A family of Cauchy-Dirichlet problems for the wave equations in unbounded domains $\Lambda_{\varepsilon}$ is considered (here $\varepsilon\geqslant 0$ is a small parameter); a scattering operator $\mathbb{S}_{\varepsilon}$ is associated with each domain $\Lambda_\varepsilon$. For $\varepsilon>0$ the boundaries of $\Lambda_{\varepsilon}$ are smooth, whilw the boundary of the limit domain $\Lambda_{0}$ contains a conical point. The asymptotics of $\mathbb{S}_{\varepsilon}$ as $\varepsilon\to 0$ is determined. Bibliography: 11 titles.
Keywords: wave equation, singularly perturbed domains, scattering operator. 
@article{SM_2021_212_10_a3,
     author = {D. V. Korikov},
     title = {Asymptotics of the scattering operator for the wave equation in a~singularly perturbed domain},
     journal = {Sbornik. Mathematics},
     pages = {1436--1470},
     publisher = {mathdoc},
     volume = {212},
     number = {10},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_10_a3/}
}
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D. V. Korikov. Asymptotics of the scattering operator for the wave equation in a~singularly perturbed domain. Sbornik. Mathematics, Tome 212 (2021) no. 10, pp. 1436-1470. http://geodesic.mathdoc.fr/item/SM_2021_212_10_a3/