# Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures

@inproceedings{Bernhoff2022LinearizedBC, title={Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures}, author={Niclas Bernhoff}, year={2022} }

Abstract: The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for monatomic single species is a classical result, while corresponding result for mixtures is more recently obtained. In this work the compactness of the operator for polyatomic single species, where the polyatomicity is modeled by a discrete internal energy…

## 5 Citations

### Linearized Boltzmann Collision Operator: II. Polyatomic Molecules Modeled by a Continuous Internal Energy Variable

- Mathematics
- 2022

: The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator.…

### Global bounded solutions to the Boltzmann equation for a polyatomic gas

- Mathematics
- 2022

. In this paper we consider the Boltzmann equation modelling the motion of a poly- atomic gas where the integration collision operator in comparison with the classical one involves an additional…

### Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

### Linear Half-Space Problems in Kinetic Theory: Abstract Formulation and Regime Transitions

- Physics
- 2022

Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen…

### Compactness property of the linearized Boltzmann collision operator for a multicomponent polyatomic gas

- Mathematics
- 2022

The linearized Boltzmann collision operator is fundamental in many studies of the Boltzmann equation and its main properties are of substantial importance. The decomposition into a sum of a positive…

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