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First mixed problem for a nonstrictly hyperbolic equation of the third order in a bounded domain

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Abstract

We study the classical solution of a boundary value problem for a nonstrictly parabolic equation of the third order in a rectangular domain of two independent variables. We pose Cauchy conditions on the lower base of the domain and the Dirichlet conditions on the lateral boundary. By the method of characteristics, we obtain a closed-form analytic expression for the solution of the problem. The uniqueness of the solution is proved.

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Authors and Affiliations

  1. Belarus State University, Minsk, Belarus

    V. I. Korzyuk & A. A. Mandrik

Authors
  1. V. I. Korzyuk
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  2. A. A. Mandrik
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Correspondence to V. I. Korzyuk.

Additional information

Original Russian Text © V.I. Korzyuk, A.A. Mandrik, 2016, published in Differentsial’nye Uravneniya, 2016, Vol. 52, No. 6, pp. 788–802.

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Korzyuk, V.I., Mandrik, A.A. First mixed problem for a nonstrictly hyperbolic equation of the third order in a bounded domain. Diff Equat 52, 767–780 (2016). https://doi.org/10.1134/S0012266116060070

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  • DOI: https://doi.org/10.1134/S0012266116060070

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