Solution of equations related to physical kinetics
Abstract
The paper is concerned with a class of nonlinear operator Volterra equations containing the kinetic Boltzmann equation for pseudo-Maxwellian molecules written in integral form. Sufficient conditions for the unique solvability of the equation as a whole in the vicinity of zero are determined. For the Smolukhovskii kinetic equation of spatially inhomogeneous coagulation, conditions are determined which produce a singularity of the 'gradient catastrophy' type in the solution due to the interaction between free particle transfer and collisions.
- Publication:
-
Akademiia Nauk SSSR Doklady
- Pub Date:
- 1988
- Bibcode:
- 1988DoSSR.298.1362G
- Keywords:
-
- Kinetic Theory;
- Molecular Physics;
- Nonlinear Equations;
- Volterra Equations;
- Boltzmann Transport Equation;
- Kinetic Equations;
- Operators (Mathematics);
- Theorem Proving;
- Thermodynamics and Statistical Physics