Abstract
We investigate the generalized solvability of a Sobolev problem. Energy inequalities in negative and positive norms are obtained. Existence and uniqueness theorems are proved for the case when the right-hand side of the equations belongs to the space of square summable functions or to some negative space.
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S. A. Gal'pern, “Cauchy problem for systems of linear partial differential equations,” Dokl. Akad. Nauk SSSR,19, No. 4, 725–728 (1958).
T. I. Zelenyak, “On behavior of solutions of one Sobolev problem as t→∞,” Dokl. Akad. Nauk SSSR,139 No. 3, 531–533 (1961).
A. G. Kostyuchenko and G. I. Eskin, “Cauchy problem for Sobolev-Galpern equations,” Tr. Mosk. Mat. Ova.,10, 273–285 (1961).
I. I. Lyashko, V. P. Didenko, and O. E. Tsitritskii, Noise Filtering [in Russian], Naukova Dumka, Kiev (1979).
S. L. Sobolev, “A new problem of mathematical physics,” Izv. Akad. Nauk SSSR, Mat.,18, No. 1, 3–50 (1954).
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 49–57, 1985
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Vityuk, N.Y. Existence and uniqueness of the solution of a Sobolev problem. J Math Sci 54, 792–799 (1991). https://doi.org/10.1007/BF01097589
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DOI: https://doi.org/10.1007/BF01097589