Open AccessАсимптотика ядер интеграла столкновений линейного уравнения Больцмана при больших значениях индекса для потенциала твердых шаров
Author(s) -
Л.А. Бакалейников,
Э.А. Тропп,
Е.Ю. Флегонтова
Publication year - 2018
Publication title -
pisʹma v žurnal tehničeskoj fiziki
Language(s) - English
Resource type - Journals
eISSN - 1726-7471
pISSN - 0320-0116
DOI - 10.21883/pjtf.2018.16.46474.17379
Subject(s) - legendre polynomials , exponent , boltzmann equation , exponential function , physics , power law , mathematical analysis , mathematics , collision , mathematical physics , quantum mechanics , statistics , computer science , philosophy , linguistics , computer security
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.