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On boundary and initial values of solutions of a second-order parabolic equation that degenerate on the domain boundary

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Abstract

Properties of the solutions of a parabolic equation in the case of a Keldysh-type degeneracy on the boundary of the domain are investigated. The unique solvability of the first mixed problem for this equation is studied. Necessary and sufficient conditions for the existence of limits of the solution on the lateral surface of a cylindrical domain and on its lower base in L2-type spaces are found.

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Authors and Affiliations

  1. Moscow Power Engineering Institute, Moscow, 111250, Russia

    I. M. Petrushko

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  1. I. M. Petrushko
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Correspondence to I. M. Petrushko.

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Original Russian Text © I.M. Petrushko, 2017, published in Doklady Akademii Nauk, 2017, Vol. 477, No. 2, pp. 150–152.

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Petrushko, I.M. On boundary and initial values of solutions of a second-order parabolic equation that degenerate on the domain boundary. Dokl. Math. 96, 568–570 (2017). https://doi.org/10.1134/S1064562417060084

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  • DOI: https://doi.org/10.1134/S1064562417060084

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