SOME UNSOLVED PHYSICAL KINETICS PROBLEMS
Abstract
A class of steady-state problems with a particle source for physical kinetics equations including Boltzmann-type collision operators. An algorithm for constructing dissipative solutions that finds exact Smoluchowski non-stationary equation solutions for spatially homogenous systems with a multiplicative particle fusion core has been proposed. The algorithm has been justified. Ai important feature of the solution class is that the collision operator is discontinuous in the permanence relation. The problem of such solution existence for Boltzmann collision operator and gas kinetic theory has been proposed. It would enable to introduce dissipative solutions to the A. V. Bobylev class of exact solutions.
Keywords
физическая кинетика,
операторы столкновений Больцмана и Смолуховского,
разрывные операторы,
законы сохранения,
точные решения,
диссипативные решения,
physical kinetics,
Boltzmann and Smoluchowski collision operators,
discontinuous operators,
laws of conservation,
exact solutions,
dissipative solutions
About the Author
V. A. Galkin
Surgut State University; System Research Institute, Russian Academy of Sciences
Russian Federation
Russian Federation
References
1. Галкин В. А. Анализ математических моделей: системы законов сохранения. Уравнения Больцмана и Смолуховского. М. : БИНОМ, 2009. 408 с.
2. Бобылев А. В. О точных решениях уравнения Больцмана // Докл. АН СССР. Т. 225. № 6. С. 1296- 1299.
3. Бобылев А. В. Об одном классе инвариантных решений уравнения Больцмана // Докл. АН СССР. Т. 231. № 3. С. 571-574.
Review
For citations:
Galkin V.A. SOME UNSOLVED PHYSICAL KINETICS PROBLEMS. Proceedings in Cybernetics. 2017;(1 (25)):34-39.
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