Free boundary methods and non-scattering phenomena
| Autor: | Mikko Salo, Henrik Shahgholian |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
FOS: Physical sciences
Boundary (topology) 01 natural sciences inversio-ongelmat Theoretical Computer Science Mathematics - Analysis of PDEs Mathematics (miscellaneous) Converse FOS: Mathematics Point (geometry) 0101 mathematics Mathematical Physics Complement (set theory) Mathematics osittaisdifferentiaaliyhtälöt Quadrature domains Scattering Applied Mathematics Research 010102 general mathematics Mathematical analysis Mathematical Physics (math-ph) 010101 applied mathematics Computational Mathematics Obstacle Inverse scattering problem Analysis of PDEs (math.AP) |
| Zdroj: | Research in the Mathematical Sciences |
| ISSN: | 2197-9847 2522-0144 |
| Popis: | We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point. These facts are proved by invoking results from the theory of free boundary problems. Comment: 18 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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