Contact-Boundary Value Problem in the Non-Classical Treatment for One Pseudo-Parabolic Equation

Ilgar G. Mamedov^1,

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

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

Abstract

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 W_p^(4,4)(G).

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

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