Exact solutions of a nonlinear Boltzmann kinetic equation with a source are constructed in the case of an isotropic distribution function and Maxwell model of isotropic scattering. These solutions are constructed with the use of an equivalence group such that one of its transformations uniquely identifies the class of the source functions that are linear in terms of the distribution function; moreover, the transformed equation has a zero right side. As a result, invariant solutions of the type of the Bobylev–Krook–Wu solutions can be explicitly found, in particular, those that admit physical interpretation.
|Number of pages||8|
|Journal||Journal of Applied Mechanics and Technical Physics|
|Publication status||Published - 1 Mar 2018|
- Boltzmann equation
- invariant solutions
- isotropic distribution function
- source function