Asymptotic behavior of the solutions for the Laplace equation with a large spectral parameter and the inhomogeneous Robin type conditions. (English) Zbl 1403.35191
The authors consider the Helmholtz equation (with constant index of refraction) in a bounded three-dimensional hollow (i.e. doubly connected) domain with inhomogeneous Robin boundary conditions on the two components of the boundary of the domain. Using single-layer potentials they obtain the (leading) asymptotic behavior of the solution as the real part of the (complex) frequency \(\lambda\) approaches infinity.
Reviewer: Vassilis G. Papanicolaou (Athena)
MSC:
| 35P25 | Scattering theory for PDEs |
| 35L05 | Wave equation |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
Laplace equation with a large spectral parameter; Helmholtz equation; inhomogeneous Robin type conditions; asymptotic; single-layer potentialsReferences:
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