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

Greens 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
Received: 19.10.2018

Citation: M. A. Lyalinov, “Greens 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 Greens 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}


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