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Transmission problem for odd-order differential equations with two time variables and a varying direction of evolution

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Abstract

The solvability of a boundary value problem for the differential equation \(h\left( x \right){u_t} + {\left( { - 1} \right)^m}\frac{{{\partial ^{2m + 1}}u}}{{\partial {a^{2m + 1}}}} - {u_{xx}} = f\left( {x,t,a} \right)\) is studied in the case where h(x) has a jump discontinuity and reverses its sign on passing through the discontinuity point. Existence and uniqueness theorems are proved in the case of solutions having all Sobolev generalized derivatives involved in the equation.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. I. Kozhanov

  2. Research Institute of Mathematics, Ammosov North-Eastern Federal University, Yakutsk, 677000, Russia

    S. V. Potapova

Authors
  1. A. I. Kozhanov
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  2. S. V. Potapova
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Corresponding author

Correspondence to A. I. Kozhanov.

Additional information

Original Russian Text © A.I. Kozhanov, S.V. Potapova, 2017, published in Doklady Akademii Nauk, 2017, Vol. 474, No. 6, pp. 661–664.

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Kozhanov, A.I., Potapova, S.V. Transmission problem for odd-order differential equations with two time variables and a varying direction of evolution. Dokl. Math. 95, 267–269 (2017). https://doi.org/10.1134/S1064562417030231

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  • DOI: https://doi.org/10.1134/S1064562417030231

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