scholarly journals A Fast Spectral Method for the Boltzmann Collision Operator with General Collision Kernels

2017 ◽  
Vol 39 (4) ◽  
pp. B658-B674 ◽  
Author(s):  
Irene M. Gamba ◽  
Jeffrey R. Haack ◽  
Cory D. Hauck ◽  
Jingwei Hu
Keyword(s):  
Spectral Method ◽  
Collision Operator ◽  
Boltzmann Collision Operator ◽  
Collision Kernels

scholarly journals Some Estimates on the Boltzmann Collision Operator

1997 ◽  
Vol 07 (07) ◽  
pp. 1023-1033 ◽  
Author(s):  
Jens Struckmeier
Keyword(s):  
Density Function ◽  
Interaction Potential ◽  
Hard Sphere ◽  
Collision Operator ◽  
Gain Term ◽  
Boltzmann Collision Operator ◽  
Maxwellian Molecules ◽  
Collision Kernels ◽  
Loss Term

The paper presents some new estimates on the gain term of the Boltzmann collision operator. For Maxwellian molecules, it is shown that the L∞-norm of the gain term can be bounded in terms of the L1- and L∞-norm of the density function f. In the case of more general collision kernels, like the hard-sphere interaction potential, the gain term is estimated pointwise by the L∞-norm of the density function and the loss term of the Boltzmann collision operator.

Moments of the Boltzmann collision operator for Coulomb interactions

2021 ◽  
Vol 28 (7) ◽  
pp. 072113
Author(s):  
Jeong-Young Ji ◽  
Min Uk Lee ◽  
Eric D. Held ◽  
Gunsu S. Yun
Keyword(s):  
Collision Operator ◽  
Coulomb Interactions ◽  
Boltzmann Collision Operator

On the Inversion of the Linearized Collision Operator

1981 ◽  
Vol 36 (2) ◽  
pp. 113-120 ◽  
Author(s):  
Ulrich Weinert
Keyword(s):  
Kernel Function ◽  
Inverse Operator ◽  
Integral Kernel ◽  
Collision Operator ◽  
Boltzmann Collision Operator ◽  
Linearized Collision Operator

Abstract Some features are discussed in connection with the representation of the linearized Boltzmann collision operator and its inversion. It is shown that under certain assumptions the inverse operator can be given explicitly as an integral kernel function.

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