Poisson relation for the scattering kernel and inverse scattering by obstacles. (English) Zbl 0888.58070

Stoyanov, L.

Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau Sémin. 1994-1995, Exp. No. 5, 10 p. (1995).

The author considers the Dirichlet problem for the wave equation in the exterior of a compact obstacle in \(\mathbb{R}^n,\) where \(n\) is odd and \(n\geq 3.\) It is shown that in a certain class of obstacles, the singularities of the scattering amplitude provide enough information to recover the obstacle. A special case of this result was proved in [V. Petkov and L. Stoyanov, Ann. Inst. H. Poincaré, Phys. Théor. 62, No. 1, 17-45 (1995; Zbl 0838.35093)].

Reviewer: T.Aktosun (Fargo)

MSC:

58J50	Spectral problems; spectral geometry; scattering theory on manifolds
35P25	Scattering theory for PDEs
35Q30	Navier-Stokes equations

Keywords:

spectral geometry; inverse obstacle scattering; geometric scattering theory

Citations:

Zbl 0838.35093