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 Zap. Nauchn. Sem. POMI, 2018, Volume 471, Pages 150–167 (Mi znsl6631)

Green’s function for the Helmholtz equation in a polygonal domain of special form with ideal boundary conditions

M. A. Lyalinov

St. Petersburg State University, St. Petersburg, Russia

Abstract: A formal approach for the construction of the Green's function in a polygonal domain with the Dirichlet boundary conditions is proposed. The complex form of the Kontorovich–Lebedev transform and reduction to a system of integral equations is exploited. The far-field asymptotics of the wave field is discussed.

Key words and phrases: diffraction by a double wedge with polygonal boundary, scattering diagram, integral equations of the second kind, Kontorovich–Lebedev transform, Sommerfeld integral.

 Funding Agency Grant Number Russian Foundation for Basic Research 17-01-00668a

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English version:
Journal of Mathematical Sciences (New York), 2019, 243:5, 734–745

UDC: 517.9

Citation: M. A. Lyalinov, “Green’s function for the Helmholtz equation in a polygonal domain of special form with ideal boundary conditions”, Mathematical problems in the theory of wave propagation. Part 48, Zap. Nauchn. Sem. POMI, 471, POMI, St. Petersburg, 2018, 150–167; J. Math. Sci. (N. Y.), 243:5 (2019), 734–745

Citation in format AMSBIB
\Bibitem{Lya18} \by M.~A.~Lyalinov \paper Green’s function for the Helmholtz equation in a~polygonal domain of special form with ideal boundary conditions \inbook Mathematical problems in the theory of wave propagation. Part~48 \serial Zap. Nauchn. Sem. POMI \yr 2018 \vol 471 \pages 150--167 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6631} \transl \jour J. Math. Sci. (N. Y.) \yr 2019 \vol 243 \issue 5 \pages 734--745 \crossref{https://doi.org/10.1007/s10958-019-04575-5} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85075161001}