On the nonlinear, spatially homogeneous Boltzmann equation with an external source: Exact generating functions for all moments
Abstract
A moment method is applied to a model Boltzmann equation including an isotropic external source. The associated infinite system of first-order differential equations for the moments is solved exactly to the extent that analytical expressions for the generating function of the moments are derived. Due to a consequent application of Lie group methods the resulting functions are of the similarity form. Certain restrictions upon the shape of the source term arising from the solution strategy are discussed.
- Publication:
-
Zeitschrift Angewandte Mathematik und Physik
- Pub Date:
- November 1986
- DOI:
- 10.1007/BF00953675
- Bibcode:
- 1986ZaMP...37..837D
- Keywords:
-
- Boltzmann Distribution;
- Distribution Functions;
- Method Of Moments;
- Nonlinear Equations;
- Abel Function;
- Differential Equations;
- Eigenvalues;
- Integral Equations;
- Integral Transformations;
- Lie Groups;
- Similarity Theorem;
- Velocity Distribution;
- Thermodynamics and Statistical Physics;
- Differential Equation;
- Generate Function;
- Mathematical Method;
- Source Term;
- Boltzmann Equation