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In this paper we consider initial-boundary problems with integral conditions for certain fourth order equation. Unique solvability of posed problems is proved. The proof is based on apriori estimates, regularization method, auxiliary problems method, embedding theorems.

About the authors

V. B. Dmitriev

Samara College of railway transport. A.
A. Buyanova, Samara, 443066, Russian Federation.

Author for correspondence.
Email: morenov.sv@ssau.ru


  1. Kozhanov A.I., L. S. Pulkina L.S. On the solvability of boundary value problems with nonlocal boundary conditions of integral form for multidimensional hyperbolic equations. Differents. Equation, 2006, Vol. 42, no. 9, pp. 1166-1179.
  2. Kozhanov A.I. On the solvability of some spatial nonlocal problems for linear parabolic equations. Vestnik SamSU, 2008, no. 3(62), pp. 165–174.
  3. Pulkina L.S. Initial boundary value problem with a nonlocal boundary condition for a multidimensional hyperbolic equation. Differents. Equation, 2008, Vol. 44, no. 8, pp. 1084-1089.
  4. Egorov I. E., Fedorov V. E. Nonclassical equations of mathematical physics. Publishing house SB RAS computing center, Novosibirsk, 1995. 133 C. 1.
  5. Kozhanov A. I. Composite Type Equations and Inverse Problems. VSP. Utrecht, 1999.
  6. Kozhanov A. I. On the solvability of the first initial-boundary value problem for a class of degenerate Sobolev type equations of high order. Nonclassical equations of mathematical physics. Sat. sci. works. Novosibirsk: Publishing house of Institute of mathematics of SB RAS, 2007, pp. 172-181.
  7. Harding L. The Cauchy Problem for hyperbolic equations. M., 1961, 122 p.
  8. Kozhanov A. I., Pulkina L. S. On the solvability of boundary value problems with nonlocal boundary condition of integral form for multidimensional hyperbolic equations. Doklady mathematics, Vol. 404, no. 5, 2005.
  9. Ladyzhenskaya O. A. Boundary value problems of mathematical physics. M.: Nauka, 1973, 408 p.
  10. Ladyzhenskaya O. A., Solonnikov V. A., Ural’tseva N. N. Linear and quasilinear equations of parabolic type. M.: "Nauka”, 1967, 736 p.
  11. Pontryagin L. S. Ordinary differential equations . Ed. 4th. M.: "Nauka”, 1974, 331.
  12. Besov O. V., Il’in V. P., Nikolsky S. M. Integral representations of functions and embedding theorems. M.: Nauka, 1975. 480 S.
  13. Yakubov S.Y. Linear differential-operator equations and their applications. Baku: Elm Press, 1985.

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Copyright (c) 2016 Dmitriev V.B.

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