Geodesic
Solution of mixed problems on diffraction of non stationary plane and cylinder waves on a half-plane and explosion waves protection by barriers
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2020), pp. 58-62 
M. Sh. Israilov; S. E. Nosov; M.-R. B. Khadisov. Solution of mixed problems on diffraction of non stationary plane and cylinder waves on a half-plane and explosion waves protection by barriers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2020), pp. 58-62. http://geodesic.mathdoc.fr/item/VMUMM_2020_3_a10/
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     author = {M. Sh. Israilov and S. E. Nosov and M.-R. B. Khadisov},
     title = {Solution of mixed problems on diffraction of non stationary plane and cylinder waves on a half-plane and explosion waves protection by barriers},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {58--62},
     year = {2020},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_3_a10/}
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Exact analytical solutions of diffraction problems are obtained for nonstationary plane and cylindrical waves on a half-plane when the following mixed boundary conditions are given: the Neumann condition on one side of the half-plane and the Dirichlet condition on the other one. The numerical analysis of near-front asymptotic solutions shows that there is a considerably greater weakening (attenuation) of explosive waves behind the half-plane (barrier) with sides of the different noise absorption properties, than under full reflection from both sides of the half-plane.

[1] Rawlins A. D., “The solution of a mixed boundary value problem in the theory of diffraction by a semi-infinite plane”, Proc. Roy. Soc. London. Ser. A, 346 (1975), 469–484 | MR | Zbl

[2] Rottbrand K., “Time-dependent plane wave diffraction by a half-plane: explicit solution for Rawlins' mixed initial boundary value problem”, Z. angew. Math. und Mech. (ZAMM), 78:5 (1998), 321–334 | 3.0.CO;2-E class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[3] Sobolev S. L., “Nekotorye voprosy teorii rasprostraneniya kolebanii”: Frank F., Mizes R., Differentsialnye i integralnye uravneniya matematicheskoi fiziki, v. 2, ONTI, M.–L., 1937, 468–617

[4] Filippov A. F., “Difraktsiya proizvolnoi akusticheskoi volny na kline”, Prikl. matem. i mekhan., 28:2 (1964), 305–318 | Zbl

[5] Friedlander F., Sound pulses, University Press, Cambridge, 1958 ; Fridlender F., Zvukovye impulsy, IL, M., 1962 | MR | Zbl

[6] Morse Ph.M., Ingard K. U., Theoretical acoustics, McGraw-Hill Book Co. Inc., N. Y., 1968

[7] Israilov M. Sh., “Exact solutions of problems of diffraction of unsteady waves on a wedge under mixed boundary conditions”, Doklady Physics, 64:4 (2019), 165–168 | DOI

[8] Israilov M. Sh., Dinamicheskaya teoriya uprugosti i difraktsiya voln, Izd-vo MGU, M., 1992

[9] Yakovlev Yu. S., Gidrodinamika vzryva, Sudpromgiz, L., 1961