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
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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) .
Final-Boundary Value Problem, Pseudoparabolic Equations, Equations with Discontinuous Coefficients
To cite this article
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. doi: 10.11648/j.acm.20130203.15
D.Colton, "Pseudoparabolic equations in one space variable", J. Different. equations, 1972, vol.12, No3, pp.559-565.
A.P.Soldatov, M.Kh.Shkhanukov, "Boundary value problems with A.A.Samarsky general nonlocal condition for higher order pseudoparabolic equations", Dokl. AN SSSR, 1987, vol.297, No 3. pp.547-552 .
A.M.Nakhushev, Equations of mathematical biology. M.: Visshaya Shkola, 1995, 301p.
S.S.Akhiev, "Fundamental solution to some local and non - local boundary value problems and their representations ", DAN SSSR, 1983, vol.271, No 2, pp.265-269.
V.I.Zhegalov, E.A.Utkina, "On a third order pseudoparabolic equation", Izv. Vuzov, Matem., 1999, No 10, pp.73-76.
I.G.Mamedov, " A fundamental solution to the Cauchy problem for a fourth- order pseudoparabolic equation",Computational Mathematics and Mathematical Physics, 2009, volume 49, Issue 1, pp 93-104.
I.G.Mamedov, "A non-classical formula for integration by parts related to Goursat problem for a pseudoparabolic equation", Vladikavkazsky Matematicheskiy Zhurnal ,2011, vol.13, No 4, pp.40-51.
I.G.Mamedov, "Goursat non - classic three dimensional problem for a hyperbolic equation with discontinuous coefficients", Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, 2010, No 1 (20), pp. 209-213.
I.G.Mamedov, "Final-boundary value problem for a hyperbolic equation with multi triple characteristics", Functional analysis and its applications, Proc. of the International Conference devoted to the centenary of acad. Z.I.Khalilov,Baku,2011,pp.232-234.
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