3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients
Applied and Computational Mathematics
Volume 4, Issue 1-1, January 2015, Pages: 1-5
Received: Apr. 21, 2014;
Accepted: Jun. 22, 2014;
Published: Jun. 30, 2014
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Ilgar Gurbat oglu Mamedov, Institute of Control Systems Azerbaijan National Academy of Sciences, Baku, Azerbaijan Republic
In this paper substantiated for a Manjeron generalized equation with non-smooth coefficients a three dimensional Goursat problem -3D Goursat problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions three dimensional boundary condition is substantiated classical, in the case if the solution of the problem in the isotropic S. L. Sobolev's space is found. The considered equation as a hyperbolic 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 3D Goursat boundary conditions in the classic and non-classic treatment are equivalent to each other. Thus, namely in this paper, the non-classic problem with 3D Goursat conditions is grounded for a hyperbolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev isotropic space.W_p^((2,2,2) ) (G)
Ilgar Gurbat oglu Mamedov,
3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients, Applied and Computational Mathematics. Special Issue: New Orientations in Applied and Computational Mathematics.
Vol. 4, No. 1-1,
2015, pp. 1-5.
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”, DAN USSR, 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 USSR, 1983, vol.271, No 2, pp.265-269.
S.S. Akhiev, “Riemann function equation with dominant mixed derivative of arbitrary order”, DAN USSR, 1985, vol. 283, No 4, pp.783-787.
V.I. Zhegalov, E.A.Utkina, “On a third order pseudoparabolic equation”, Izv. Vuzov, Matem., 1999, No 10, pp.73-76.
I. G. 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
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, “Nonlocal combined problem of Bitsadze-Samarski and Samarski-Ionkin type for a system of pseudoparabolic equations ”, Vladikavkazsky Matematicheskiy Zhurnal ,2014, vol.16, No 1, pp.30-41.
I.G. Mamedov, “On a nonclassical interpretation of the Dirichlet problem for a fourth-order pseudoparabolic equation“, Differential Equations, 2014, vol. 50, №3, pp. 415-418.
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.