Geodesic
An over-determined boundary problem for the Helmholtz equation in a~semifinite domain with a~curvilinear boundary
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 77-85

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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, space of slow-growth distributions.
Mots-clés : Fourier transform 
@article{IVM_2010_2_a7,
     author = {D. N. Tumakov},
     title = {An over-determined boundary problem for the {Helmholtz} equation in a~semifinite domain with a~curvilinear boundary},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {77--85},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_2_a7/}
}
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D. N. Tumakov. An over-determined boundary problem for the Helmholtz equation in a~semifinite domain with a~curvilinear boundary. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 77-85. http://geodesic.mathdoc.fr/item/IVM_2010_2_a7/