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The dirichlet problem for a loaded mixed-type equation in a rectangular domain

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Abstract

We establish necessary and sufficient conditions for the unique solvability of the first boundary problem for a loaded equation with the Lavrent’ev-Bitsadze operator in a rectangular domain. We obtain a solution to the stated problem as the sum of the eigenfunction series for the corresponding one-dimensional problem with respect to eigenvalues. We prove the stability of the solution with respect to boundary functions.

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Authors and Affiliations

  1. Samara State Academy of Social Sciences and Humanities, ul. Antonova-Ovseenko 26, Samara, 443090, Russia

    K. B. Sabitov & E. P. Melisheva

Authors
  1. K. B. Sabitov
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  2. E. P. Melisheva
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Correspondence to K. B. Sabitov.

Additional information

Original Russian Text © K.B. Sabitov and E.P. Melisheva, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 7, pp. 62–76.

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Sabitov, K.B., Melisheva, E.P. The dirichlet problem for a loaded mixed-type equation in a rectangular domain. Russ Math. 57, 53–65 (2013). https://doi.org/10.3103/S1066369X13070062

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  • DOI: https://doi.org/10.3103/S1066369X13070062

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