Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation
Applied and Computational Mathematics
Volume 2, Issue 3, June 2013, Pages: 96-99
Received: Jun. 24, 2013;
Published: Jul. 20, 2013
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Ilgar Gurbat oglu Mamedov, Institute of Cybernetics Azerbaijan National Academy of Sciences, B. Vahabzade St.9, Baku city, AZ 1141, Azerbaijan Republic
In this paper substantiated for a differential equation of pseudoparabolic type with discontinuous coefficients a final-boundary problem with non-classical boundary conditions is considered, which requires no matching conditions. The considered equation as a pseudoparabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation , moisture transfer generalized equation, Manjeron equation, Boussinesq-Love equation and etc.). It is grounded that the final-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 final-boundary conditions is grounded for a pseudoparabolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev anisotropic space WP(4,2)(G) .
Ilgar Gurbat oglu Mamedov,
Final-Boundary Value Problem in the Non-Classical Treatment for a Sixth Order Pseudoparabolic Equation, Applied and Computational Mathematics.
Vol. 2, No. 3,
2013, pp. 96-99.
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