Abstract
Under consideration is the second boundary value problem in a half-space for the Navier system.We provide some necessary conditions for unique solvability in Sobolev spaces.
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References
I. N. Vekua, Some General Methods for Construction of Various Variants of Shell Theory (Nauka, Moscow, 1982) [in Russian].
G. V. Demidenko, “On Solvability of Boundary Value Problems for Quasi-Elliptic Systems in Rn +,” J. Anal. Appl. 4 (1), 1–11 (2006).
L. N. Bondar, “Conditions for the Solvability ofBoundaryValue Problems forQuasi-Elliptic Systems in aHalf-Space,” Differentsial’nyeUravneniya 48 (3), 341–350 (2012) [Differential Equations 48 (3), 343–353 (2012)].
G. V. Demidenko, “Integral Operators Determined by Quasielliptic Equations. II,” Sibir. Mat. Zh. 35 (1), 41–65 (1994) [SiberianMath. J. 35 (1), 37–61 (1994)].
G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems Not Solvable with Respect to the Highest-Order Derivative (Nauchnaya Kniga, Novosibirsk, 1998;Marcel Decker,New York, 2003).
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Original Russian Text © L.N. Bondar, 2018, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2018, Vol. XXI, No. 4, pp. 3–14.
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Bondar, L.N. Solvability Conditions for the Second Boundary Value Problem for the Navier System. J. Appl. Ind. Math. 12, 595–606 (2018). https://doi.org/10.1134/S1990478918040014
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DOI: https://doi.org/10.1134/S1990478918040014