Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions
| Autor: | Yerkanat Auzhani, Auzhan Sakabekov |
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| Rok vydání: | 2016 |
| Předmět: |
Article Subject
lcsh:Mathematics Applied Mathematics Mathematical analysis 010103 numerical & computational mathematics lcsh:QA1-939 01 natural sciences 010101 applied mathematics Moment (mathematics) Method of undetermined coefficients Nonlinear system symbols.namesake Boltzmann constant Riccati equation symbols Initial value problem Uniqueness Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | J. Appl. Math. Journal of Applied Mathematics, Vol 2016 (2016) |
| ISSN: | 1687-0042 1110-757X |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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