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Eurasian Mathematical Journal, 2017, Volume 8, Number 1, Pages 50–57
(Mi emj247)
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This article is cited in 3 scientific papers (total in 3 papers)
On an ill-posed problem for the Laplace operator with nonlocal boundary condition
T. Sh. Kal'menov, B. T. Torebek Institute of Mathematics and Mathematical Modeling,
125 Pushkin St, 050010 Almaty, Kazakhstan
Abstract:
In this paper a nonlocal problem for the Poisson equation in a rectangular is considered. It is shown that this problem is ill-posed as well as the Cauchy problem for the Laplace equation. The method of spectral expansion via eigenfunctions of the nonlocal problem for equations with deviating argument allows us to establish a criterion of the strong solvability of the considered nonlocal problem. It is shown that the ill-posedness of the nonlocal problem is equivalent to the existence of an isolated point of the continuous spectrum for a nonself-adjoint operator with the deviating argument.
Keywords and phrases:
Laplace operator, nonlocal boundary value problem, differential operator, criterion of well-posedness.
Received: 28.11.2016
Citation:
T. Sh. Kal'menov, B. T. Torebek, “On an ill-posed problem for the Laplace operator with nonlocal boundary condition”, Eurasian Math. J., 8:1 (2017), 50–57
Linking options:
https://www.mathnet.ru/eng/emj247 https://www.mathnet.ru/eng/emj/v8/i1/p50
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Abstract page: | 584 | Full-text PDF : | 361 | References: | 221 |
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