Group analysis of the Fourier transform of the spatially homogeneous and isotropic Boltzmann equation with a source term
| Autor: | Yurii N. Grigoriev, A. Suriyawichitseranee, Sergey V. Meleshko |
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| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Partial differential equation 76M60 76P05 Differential equation Applied Mathematics Mathematical analysis First-order partial differential equation FOS: Physical sciences Mathematical Physics (math-ph) Boltzmann equation Screened Poisson equation symbols.namesake Homogeneous differential equation Integro-differential equation Modeling and Simulation symbols Fisher's equation Mathematical Physics Mathematics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 20:719-730 |
| ISSN: | 1007-5704 |
| DOI: | 10.1016/j.cnsns.2014.06.047 |
| Popis: | The paper is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. Using a particular class of solutions, the determining equation for the admitted Lie group is reduced to a partial differential equation for the source function. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation is given. All invariant solutions of this equation are also presented in the paper. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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