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The basis for an operational method of solving certain problems in mathematical physics

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Abstract

In this paper we obtain sufficient conditions for the applicability of an operational method for solving a mixed problem for an equation of parabolic type with discontinuous coefficients.

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Literature cited

  1. V. A. Ditkin and P. I. Kuznestov, Handbook on the Operational Calculus [in Russian], Moscow (1951).

  2. A. V. Ivanov, “Heat conduction problems for multi-layer media and Green's cell function,” Izv. Akad. Nauk BSSR, Ser. Fiz.-tekhn. Nauk, No. 3, 5–8 (1963).

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  3. L. F. Karaul'naya, “Birkhoff-Tamarkin's asymptotic theorem in the operational calculus,” Dokl. Akad. Nauk SSSR,196, No. 3, 506–507 (1971).

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  4. Ya. D. Tamarkin, Certain General Problems in the Theory of Ordinary Differential Equations and the Expansion of Arbitrary Functions in Series, [in Russian], Petrograd (1917).

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Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 125–134, January, 1973.

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Karaul'naya, L.F. The basis for an operational method of solving certain problems in mathematical physics. Mathematical Notes of the Academy of Sciences of the USSR 13, 74–79 (1973). https://doi.org/10.1007/BF01093635

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  • DOI: https://doi.org/10.1007/BF01093635

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