Abstract:
A model Helmholtz equation with a localized right-hand side is considered. When writing asymptotics of a solution satisfying the limit absorption principle, a Lagrangian surface naturally appears that has a logarithmic singularity at one point. Because of this singularity, the solution is localized not only in a neighborhood of the projection of the Lagrangian surface onto the coordinate space but also in a neighborhood of a certain ray “escaping” from the Lagrangian surface and going into the region forbidden in the classical approximation.
Citation:
I. A. Bogaevsky, S. Yu. Dobrokhotov, A. A. Tolchennikov, “Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side”, TMF, 218:1 (2024), 23–47; Theoret. and Math. Phys., 218:1 (2024), 19–40
\Bibitem{BogDobTol24}
\by I.~A.~Bogaevsky, S.~Yu.~Dobrokhotov, A.~A.~Tolchennikov
\paper Arnold Lagrangian singularity in the asymptotics of the solution of a model two-dimensional Helmholtz equation with a localized right-hand side
\jour TMF
\yr 2024
\vol 218
\issue 1
\pages 23--47
\mathnet{http://mi.mathnet.ru/tmf10553}
\crossref{https://doi.org/10.4213/tmf10553}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...218...19B}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 218
\issue 1
\pages 19--40
\crossref{https://doi.org/10.1134/S0040577924010021}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85179156051}
Linking options:
https://www.mathnet.ru/eng/tmf10553
https://doi.org/10.4213/tmf10553
https://www.mathnet.ru/eng/tmf/v218/i1/p23
This publication is cited in the following 2 articles: