Boundary value problems for fourth-order Sobolev type equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 425-432.

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The goal of the article is the study of solvability in the Sobolev spaces of boundary value problems for some classes of Sobolev-type fourth-order linear equations. We will prove that an initial boundary value problems well problems with data both at the initial time moment and the final time moments can be well-posed for the equations under study.
Keywords: Sobolev-type fourth-order differential equation, boundary value problem, uniqueness.
Mots-clés : existence
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Alexander I. Kozhanov. Boundary value problems for fourth-order Sobolev type equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 4, pp. 425-432. http://geodesic.mathdoc.fr/item/JSFU_2021_14_4_a3/

[1] S.L. Sobolev, “On a boundary value problem of mathematical physics”, Izv. Academy of Sciences of the USSR. Ser. Mat., 18:2 (1954), 3–50 (in Russian) | MR | Zbl

[2] G.V. Demidenko, S.V. Uspensky, Equations and systems not resolved with respect to the highest derivative, Scientific, Novosibirsk, 1998 (in Russian) | MR

[3] A.I. Kozhanov, Composite Type Equations and Inverse Problems, VSP, Utrecht, 1999 | MR | Zbl

[4] I.E. Egorov, S.G. Pyatkov, S.V. Popov, Non-classical differential-operator equations, Science, Novosibirsk, 2000 (in Russian) | MR

[5] S.G. Pyatkov, Operator Theory. Nonclassical Problems, VSP, Utrecht–Boston–Koln–Tokyo, 2002 | MR | Zbl

[6] G.A. Sviridyuk, V.E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroup of Operators, VSP, Utrecht, 2003 | MR

[7] A.G. Sveshnikov, A.B. Alshin, M.O. Korpusov, Yu.D. Pletner, Linear and nonlinear equations of the Sobolev type, Fizmatlit, M., 2007 (in Russian)

[8] V.I. Zhegalov, A.N. Mironov, E.A. Utkina, Equations with a dominant partial derivative, Kazan Federal University, Kazan, 2014 (in Russian)

[9] S.L. Sobolev, Some applications of functional analysis in mathematical physics, Science, M., 1988 (in Russian) | MR

[10] O.A. Ladyzhenskaya, N.N. Uraltseva, Linear and quasilinear equations of elliptic type, Nauka, M., 1973 (in Russian) | MR | Zbl

[11] H. Triebel, Interpolation Theory. Function Spaces. Differential Operators, VEB Deutcher Verlag der Wissenschaften, Berlin, 1978 | MR

[12] V.N. Vragov, “On the theory of boundary value problems for mixed-type equations”, Differential Equations, 13:6 (1977), 1098–1105 | MR | Zbl

[13] I.E. Egorov, V.E. Fedorov, Non-classical equations of high-order mathematical physics, Publishing house of the Computing Center SB RAS, Novosibirsk, 1995 (in Russian) | MR

[14] A.I. Kozhanov, N.R. Pinigina, “Boundary problems for some non-classical differential equations”, Math. Notes, 101:3 (2017), 467–474 | DOI | MR | Zbl

[15] V.A. Trenogin, Functional analysis, Nauka, M., 1980 | MR | Zbl

[16] A.I. Kozhanov, “Linear inverse problems for a class of degenerate equations of Sobolev type”, Vestn. SUSU. Ser. Mat. modeling and programming, 5(264):11 (2012), 33–42 | Zbl