Abstract
It is shown that the generalized Fourier transform can be extended to an arbitrary elliptic operator in a cylindrical domain with a Robin boundary condition. In this case, the existence of the Fourier image is a completely correct radiation condition determining a solution to the problem that is a superposition of waves traveling away from the source.
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Original Russian Text © A.N. Bogolubov, M.D. Malykh, Yu.V. Mukhartova, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 12, pp. 2228–2234.
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Bogolubov, A.N., Malykh, M.D. & Mukhartova, Y.V. Solution to the boundary value problem for an arbitrary elliptic operator subject to a radiation condition. Comput. Math. and Math. Phys. 46, 2129–2135 (2006). https://doi.org/10.1134/S0965542506120116
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DOI: https://doi.org/10.1134/S0965542506120116