Correctness of task family with nonclassical boundary conditions

Mokin A.Y.
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A boundary value problem for partial differential equation with nonlocal boundary relations of special type is resolved by means of a slight modification of the separation of variables method. Ordinal differential operator of the second order subject to boundary conditions of the main problem is not self-adjoint. The system of eigenfunctions generated by the operator has no basis property in L2[0,1] space. A special system of functions is proposed to expand the solution of the boundary value problem.

Keywords: nonclassical boundary conditions, parabolic type problem, separation of variables method
Citation in English: Mokin A.Y. Correctness of task family with nonclassical boundary conditions // Computer Research and Modeling, 2009, vol. 1, no. 2, pp. 139-146
Citation in English: Mokin A.Y. Correctness of task family with nonclassical boundary conditions // Computer Research and Modeling, 2009, vol. 1, no. 2, pp. 139-146
DOI: 10.20537/2076-7633-2009-1-2-139-146
URL: http://crm-en.ics.org.ru/journal/article/1558/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
According to Crossref, this article is cited by:
  • Allaberen Ashyralyev, Abdizhahan Sarsenbi. Well-posedness of a parabolic equation with nonlocal boundary condition. // Boundary Value Problems. — 2015. — V. 2015, no. 1. DOI: 10.1186/s13661-015-0297-5
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