Well-Posed Solvability of the Neumann Problem for a Generalized Mangeron Equation with Nonsmooth Coefficients

Abstract

For a fourth-order generalized Mangeron equation with nonsmooth coefficients defined on a rectangular domain, we consider the Neumann problem with nonclassical conditions that do not require matching conditions. We justify the equivalence of these conditions to classical boundary conditions for the case in which the solution to the problem is sought in an isotropic Sobolev space. The problem is solved by reduction to a system of integral equations whose well-posed solvability is established based on the method of integral representations. The well-posed solvability of the Neumann problem for the generalized Mangeron equation is proved by the method of operator equations.

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Funding

This work was supported by a grant from the Presidium of Azerbaijan National Academy of Sciences in the framework of funding scientific research for the period of 2018–2019.

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Correspondence to I. G. Mamedov or M. Dzh. Mardanov or T. K. Melikov or R. A. Bandaliev.

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Russian Text © The Author(s), 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 10, pp. 1405–1415.

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Mamedov, I.G., Mardanov, M.D., Melikov, T.K. et al. Well-Posed Solvability of the Neumann Problem for a Generalized Mangeron Equation with Nonsmooth Coefficients. Diff Equat 55, 1362–1372 (2019). https://doi.org/10.1134/S0012266119100112

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