Boundary problems for the one-dimensional kinetic equation with frequency of collisions, affine depending on the module velocity

TL;DR

This paper derives analytical solutions for temperature jump and evaporation problems in a one-dimensional kinetic model with velocity-dependent collision frequency, using the BGK collision integral.

Contribution

It introduces an analytical approach to solve kinetic equations with affine velocity-dependent collision frequency for boundary problems.

Findings

Analytical solutions for temperature jump and evaporation over flat surfaces.

Effective modeling of velocity-dependent collision frequency in kinetic equations.

Enhanced understanding of boundary phenomena in kinetic theory.

Abstract

For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and Krook) and frequency of collisions of molecules, affine depending on the module molecular velocity.