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)
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Applied and Computational Mathematics (Volume 4, Issue 1-1)
This article belongs to the Special Issue New Orientations in Applied and Computational Mathematics |
| DOI | 10.11648/j.acm.s.2015040101.11 |
| Page(s) | 1-5 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2014. Published by Science Publishing Group |
3D Goursat Problem, Manjeron Generalized Equation, Hyperbolic Equation, Equation with Non-Smooth Coefficients
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APA Style
Ilgar Gurbat oglu Mamedov. (2014). 3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients. Applied and Computational Mathematics, 4(1-1), 1-5. https://doi.org/10.11648/j.acm.s.2015040101.11
ACS Style
Ilgar Gurbat oglu Mamedov. 3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients. Appl. Comput. Math. 2014, 4(1-1), 1-5. doi: 10.11648/j.acm.s.2015040101.11
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Download@article{10.11648/j.acm.s.2015040101.11,
author = {Ilgar Gurbat oglu Mamedov},
title = {3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {1-1},
pages = {1-5},
doi = {10.11648/j.acm.s.2015040101.11},
url = {https://doi.org/10.11648/j.acm.s.2015040101.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2015040101.11},
abstract = {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)},
year = {2014}
}
TY - JOUR T1 - 3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients AU - Ilgar Gurbat oglu Mamedov Y1 - 2014/06/30 PY - 2014 N1 - https://doi.org/10.11648/j.acm.s.2015040101.11 DO - 10.11648/j.acm.s.2015040101.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 1 EP - 5 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.s.2015040101.11 AB - 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) VL - 4 IS - 1-1 ER -
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