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Boundary Value Problems for Degenerating and Nondegenerating Sobolev-Type Equations with a Nonlocal Source in Differential and Difference Forms

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Abstract

Boundary value problems are considered for degenerating and nondegenerating differential equations of the Sobolev type with a nonlocal source as well as finite-difference methods for solving these problems. A priori estimates are derived for solving the problems posed in differential and difference interpretations. These a priori estimates entail the uniqueness and stability of the solution with respect to the initial data and the right-hand side on a layer as well as the convergence of the solution of each difference problem to that of the counterpart differential problem.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, Nalchik, Kabardino-Balkariya, 360000, Russia

    M. Kh. Beshtokov

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  1. M. Kh. Beshtokov
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Correspondence to M. Kh. Beshtokov.

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Original Russian Text © M.Kh. Beshtokov, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 2, pp. 249–266.

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Beshtokov, M.K. Boundary Value Problems for Degenerating and Nondegenerating Sobolev-Type Equations with a Nonlocal Source in Differential and Difference Forms. Diff Equat 54, 250–267 (2018). https://doi.org/10.1134/S0012266118020118

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  • DOI: https://doi.org/10.1134/S0012266118020118

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