NDLI: On uniqueness and stability of Sobolev’s solution in scattering by wedges

Content Provider	Springer Nature Link
Author	Merzon, A. E. Komech, A. I. Paz Méndez, J. E. De
Copyright Year	2015
Abstract	We prove that the solution of the scattering problem of pulses, constructed by Sobolev (Proc Seismol Inst Acad Sci URSS 41:1–15, 1934), coincides with the solution obtained by our method of complex characteristics. The coincidence holds for the DD- and NN-boundary conditions. The method of complex characteristics has been developed by Komech and Merzon in 2002–2007. Its main advantage is that it provides (a) the existence and uniqueness of the solutions in suitable functional classes and (b) the limiting amplitude principle. The uniqueness in the Sobolev approach was not considered. Our result means that Sobolev’s solution belongs to our functional classes and agrees with the limiting amplitude principle.
Ending Page	2498
Page Count	14
Starting Page	2485
File Format	PDF
ISSN	00442275
e-ISSN	14209039
Journal	Zeitschrift für angewandte Mathematik und Physik
Issue Number	5
Volume Number	66
Language	English
Publisher	Springer Basel
Publisher Date	2015-05-13
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Limiting amplitude PDEs in connection with optics and electromagnetic theory Mathematical Methods in Physics Stability Diffraction, scattering Plane wave Sobolev Theoretical and Applied Mechanics Wedge Wave equation scattering Exact solution
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Physics and Astronomy

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On uniqueness and stability of Sobolev’s solution in scattering by wedges