Applied Mathematics and Physics
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Applied Mathematics and Physics. 2014, 2(2), 49-52
DOI: 10.12691/amp-2-2-4
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Contact-Boundary Value Problem in the Non-Classical Treatment for One Pseudo-Parabolic Equation

Ilgar G. Mamedov1,

1Institute of Cybernetics Azerbaijan National Academy of Sciences, Baku, Azerbaijan

Pub. Date: March 12, 2014

Cite this paper:
Ilgar G. Mamedov. Contact-Boundary Value Problem in the Non-Classical Treatment for One Pseudo-Parabolic Equation. Applied Mathematics and Physics. 2014; 2(2):49-52. doi: 10.12691/amp-2-2-4


In this paper substantiated for a differential equation of pseudo-parabolic type with discontinuous coefficients a contact-boundary value problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions boundary condition is substantiated classical, in the case if the solution of the problem in the izotropic S.L. Sobolev's space is found. The considered equation as a pseudo-parabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (Aller's equation, Manjeron equation, telegraph equation, moisture transfer generalized equation, Boussinesq - Love equation and etc.). It is grounded that the contact-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with contact-boundary conditions is grounded for a pseudo-parabolic equation. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev izotropic space Wp(4,4)(G).

Contact - boundary value problem pseudo-parabolic equation equation with discontinuous coefficients

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[1]  D. Colton, Pseudo-parabolic equations in one space variable, Different. Equations, vol. 12, No. 3, (1972), 559-565.
[2]  A.P. Soldatov, M.Kh. Shkhanukov, Boundary value problems with A.A. Samarsky general nonlocal condition for higher order pseudo-parabolic equations, Dokl. AN SSSR, vol. 297, No. 3, (1987), 547-552 (in Russian).
[3]  A.M. Nakhushev, Equations of mathematical biology, M.: Visshaya Shkola, 301p, 1995 (in Russian).
[4]  S.S. Akhiev, Fundamental solution to some local and non - local boundary value problems and their representations, DAN USSR, vol.271, No 2, (1983), 265-269 (in Russian).
[5]  V.I. Zhegalov, E.A. Utkina, on a third order pseudo-parabolic equation, Izv. Vuzov, Matem. No 10, (1999), 73-76 (in Russian).
[6]  I.G. Mamedov, A fundamental solution to the Cauchy problem for a fourth-order pseudo-parabolic equation, Springer, Computational Mathematics and Mathematical Physics, vol. 49, Issue 1, (2009), 93-104.
[7]  I.G. Mamedov, Goursat non - classic three dimensional problems for a hyperbolic equation with discontinuous coefficients, Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, Ser. Fiz.-Mat. Nauki, No. 1 (20), (2010), 209-213 (in Russian).
[8]  I.G. Mamedov, Fundamental solution of initial boundary value problem for a fourth order pseudo-parabolic equation with non-smooth coefficients, Vladikavkazskii Matematicheskii Zhurnal, vol. 12, No 1, (2010), 17-32 (in Russian).
[9]  I.G. Mamedov, A non-classical formula for integration by parts related to Goursat problem for a pseudo-parabolic equation, Vladikavkazskii Matematicheskii Zhurnal, vol. 13, No 4, (2011), 40-51 (in Russian).
[10]  I.G. Mamedov, Contact-boundary value problem for a hyperbolic equation with multiple characteristics, Functional analysis and its applications, Proceedings of the International Conference devoted to the centenary of academician Z. I. Khalilov, Baku, (2011), 230-232 (in Russian).