The parabolic equation describes the propagation of localized waves along the boundary with singularities. Some reformulation of the “separation of variables” scheme is presented, which enables us to obtain a rich set of solutions of the corresponding boundary value problems.
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Dedicated to the memory of A. P. Kachalov
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 471, 2018, pp. 124–139.
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Kazakov, A.Y. “Separation of Variables” in the Model Problems of the Diffraction Theory. A Formal Scheme. J Math Sci 243, 715–725 (2019). https://doi.org/10.1007/s10958-019-04573-7
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DOI: https://doi.org/10.1007/s10958-019-04573-7