This article is cited in 3 papers

An over-determined boundary problem for the Helmholtz equation in a semifinite domain with a curvilinear boundary

D. N. Tumakov

Department of Applied Mathematical Physics, Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia

Abstract: In this paper we consider an over-determined Cauchy problem for the Helmholtz equation in a semifinite domain with a piecewise smooth curvilinear boundary. Applying the Fourier transform method in the space of slow-growth distributions, we establish necessary and sufficient solvability conditions which connect the boundary functions. We construct integral representations of solutions.

Keywords: over-determined Cauchy problem, Helmholtz equation, Fourier transform, space of slow-growth distributions.

UDC: 517.958+537.8

Received: 17.10.2007

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:2, 66–73

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