Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions
We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/5834620 |
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| _version_ | 1832545553845583872 |
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| author | A. Sakabekov Y. Auzhani |
| author_facet | A. Sakabekov Y. Auzhani |
| author_sort | A. Sakabekov |
| collection | DOAJ |
| description | We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form. |
| format | Article |
| id | doaj-art-0c0d62fa78e34a1bb784fcf9626740ae |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-0c0d62fa78e34a1bb784fcf9626740ae2025-02-03T07:25:20ZengWileyJournal of Applied Mathematics1110-757X1687-00422016-01-01201610.1155/2016/58346205834620Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary ConditionsA. Sakabekov0Y. Auzhani1Research Laboratory “Applied Modeling Oil and Gas Fields”, Kazakh-British Technical University, 59 Tole Bi Street, Almaty 050000, KazakhstanAl-Farabi Kazakh National University, 71 Al-Farabi Avenue, Almaty 050040, KazakhstanWe prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.http://dx.doi.org/10.1155/2016/5834620 |
| spellingShingle | A. Sakabekov Y. Auzhani Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions Journal of Applied Mathematics |
| title | Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions |
| title_full | Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions |
| title_fullStr | Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions |
| title_full_unstemmed | Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions |
| title_short | Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions |
| title_sort | boltzmann s six moment one dimensional nonlinear system equations with the maxwell auzhan boundary conditions |
| url | http://dx.doi.org/10.1155/2016/5834620 |
| work_keys_str_mv | AT asakabekov boltzmannssixmomentonedimensionalnonlinearsystemequationswiththemaxwellauzhanboundaryconditions AT yauzhani boltzmannssixmomentonedimensionalnonlinearsystemequationswiththemaxwellauzhanboundaryconditions |