Abstract:
We consider the Dirichlet problem in a four-dimensional domain formed by characteristic surfaces of an equation of the 8th order with the double major partial derivative. We state sufficient conditions for the unique solvability of this problem in terms of control coefficients, basing on the method of a priori estimates.
Keywords:
Dirichlet problem, method of a priori estimates.
\Bibitem{Utk11}
\by E.~A.~Utkina
\paper A uniqueness theorem for solution of one Dirichlet problem
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 5
\pages 62--67
\mathnet{http://mi.mathnet.ru/ivm7304}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2920090}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 5
\pages 51--55
\crossref{https://doi.org/10.3103/S1066369X11050082}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051621164}
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https://www.mathnet.ru/eng/ivm7304
https://www.mathnet.ru/eng/ivm/y2011/i5/p62
This publication is cited in the following 7 articles:
Azizbayov I E., Mehraliyev Ya.T., “Inverse Boundary-Value Problem For the Equation of Longitudinal Wave Propagation With Non-Self-Adjoint Boundary Conditions”, Filomat, 33:16 (2019), 5259–5271
A. I. Grigoreva, “Zadachi sopryazheniya dlya nekotorykh analogov uravneniya prodolnykh voln s razryvnym koeffitsientom”, Chelyab. fiz.-matem. zhurn., 3:3 (2018), 276–294
Sh. Amirov, A. I. Kozhanov, “Global Solvability of Initial Boundary-Value Problems for Nonlinear Analogs of the Boussinesq Equation”, Math. Notes, 99:2 (2016), 183–191
O. S. Zikirov, “On the Dirichlet problem for hyperbolic equations of the third order”, Russian Math. (Iz. VUZ), 58:7 (2013), 53–60
Utkina E.A., “Uniqueness of the Solution of the Dirichlet Problem for an N-Dimensional Pseudoparabolic Equation”, Differ. Equ., 48:10 (2012), 1423–1428
Mamedov I., “Neumann Problem in the Non-Classical Treatment for a Fourth Order Pseudoparabolic Equation”, 2012 IV International Conference Problems of Cybernetics and Informatics (Pci), ed. AidaZade K., IEEE, 2012
Ilgar Mamedov, 2012 IV International Conference “Problems of Cybernetics and Informatics” (PCI), 2012, 1
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