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

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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.

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Authors and Affiliations

  1. Faculty of Mathematics of Vienna University, Vienna, Austria

    A. I. Komech

  2. Institute for the Information Transmission Problems of RAS, Moscow, Russia

    A. I. Komech

  3. Institute of Physics and Mathematics, University of Michoacán of San Nicolás de Hidalgo, Morelia, Michoacán, México

    A. E. Merzon

  4. Faculty of Mathematics of UAGro, Chilpancingo, Mexico

    J. E. De la Paz Méndez

Authors
  1. A. I. Komech
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  2. A. E. Merzon
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  3. J. E. De la Paz Méndez
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Corresponding author

Correspondence to A. E. Merzon.

Additional information

A. I. Komech: Supported partly by Austrian Science Fund (FWF): P22198-N13, and the Grant of RFBR, 13-01-00073.

A.E.Merzon: Supported by CONACYT, PROMEP (via Proyecto de Red), CIC (UMSNH) México.

J. E. De la Paz Méndez: Supported by CONACYT, PROMEP (via Proyecto de Red), CIC (UMSNH) México.

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Komech, A.I., Merzon, A.E. & la Paz Méndez, J.E.D. On uniqueness and stability of Sobolev’s solution in scattering by wedges. Z. Angew. Math. Phys. 66, 2485–2498 (2015). https://doi.org/10.1007/s00033-015-0533-y

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  • DOI: https://doi.org/10.1007/s00033-015-0533-y

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