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On uniqueness and stability of Sobolev’s solution in scattering by wedges
| Content Provider | Semantic Scholar |
|---|---|
| Author | Komech, Alexander Merzon, A. E. Méndez, J. E. De Paz |
| 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. |
| Starting Page | 2485 |
| Ending Page | 2498 |
| Page Count | 14 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00033-015-0533-y |
| Volume Number | 66 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s00033-015-0533-y |
| Alternate Webpage(s) | https://doi.org/10.1007/s00033-015-0533-y |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
