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On the solvability in a weighted space of an initial–boundary value problem for a third-order operator-differential equation with a parabolic principal part

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Abstract

In a Sobolev-type space with an exponential weight, sufficient conditions are obtained for the correct and unique solvability of an initial–boundary value problem for a third-order operator-differential equation with a parabolic principal part having a multiple characteristic. The conditions are expressed in terms of the operator coefficients of the equation. Additionally, the norms of the operators of intermediate derivatives associated with the solvability conditions are estimated. The relation between the weight exponent and the lower boundary of the spectrum of the basic operator involved in the principal part of the equation is established. The results are illustrated as applied to a mixed problem for partial differential equations.

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Authors and Affiliations

  1. Baku State University, ul. Z. Khalilova 23, Baku, AZ1148, Azerbaijan

    A. R. Aliev

  2. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, ul. B. Vakhabzade 9, Baku, AZ1141, Azerbaijan

    A. R. Aliev

  3. Azerbaijan State University of Oil and Industry, pr. Azadlig 20, Baku, AZ1010, Azerbaijan

    F. S. Lachinova

Authors
  1. A. R. Aliev
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  2. F. S. Lachinova
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Correspondence to A. R. Aliev.

Additional information

Original Russian Text © A.R. Aliev, F.S. Lachinova, 2016, published in Doklady Akademii Nauk, 2016, Vol. 466, No. 6, pp. 637–640.

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Aliev, A.R., Lachinova, F.S. On the solvability in a weighted space of an initial–boundary value problem for a third-order operator-differential equation with a parabolic principal part. Dokl. Math. 93, 85–88 (2016). https://doi.org/10.1134/S1064562416010294

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  • DOI: https://doi.org/10.1134/S1064562416010294

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