Time asymptotic behavior of the solution to the linear Boltzmann equation in finite bodies

2020 ◽  
Vol 31 (5-6) ◽  
pp. 1057-1079
Author(s):  
Youssouf Kosad ◽  
Khalid Latrach
Keyword(s):  
Asymptotic Behavior ◽  
Boltzmann Equation ◽  
Linear Boltzmann Equation ◽  
Time Asymptotic Behavior

scholarly journals Асимптотика ядер интеграла столкновений линейного уравнения Больцмана при больших значениях индекса для потенциала твердых шаров

2018 ◽  
Vol 44 (16) ◽  
pp. 33
Author(s):  
Л.А. Бакалейников ◽  
Э.А. Тропп ◽  
Е.Ю. Флегонтова
Keyword(s):  
Asymptotic Behavior ◽  
Boltzmann Equation ◽  
Exponential Decay ◽  
Power Law ◽  
Hard Sphere ◽  
Legendre Polynomials ◽  
Integral Operators ◽  
Collision Integral ◽  
Linear Boltzmann Equation ◽  
Interacting Particles

AbstractWe have identified the asymptotic behavior of the kernels with large indices of integral operators representing the coefficients of expansion in Legendre polynomials of the collision integral of the linear Boltzmann equation for hard-sphere potential. In the case of interacting particles with nonequal absolute values of velocities, the kernels exhibit exponential decay, where the base of the exponent contains the ratio of the lower to higher velocity. In the case of interacting particles with equal absolute values of velocities, the kernels decay according to the power law.

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