Open AccessExponential stability of the stationary solutions of the kinetic Carleman system
Author(s) -
S. A. Dukhnovskii
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1425/1/012142
Subject(s) - autocatalysis , kinetic energy , autocatalytic reaction , kinetic theory , stability (learning theory) , exponential stability , mathematics , cauchy distribution , exponential function , cauchy problem , initial value problem , mathematical analysis , thermodynamics , statistical physics , physics , classical mechanics , computer science , nonlinear system , kinetics , quantum mechanics , machine learning
In this article we discuss the kinetic system of Carleman equations. Research of technological processes for the production of building materials is based on autocatalysis reactions. The Carleman system is a special case of the discrete Boltzmann equation. In many problems of the kinetic theory of gases, gas dynamics, autocatalysis chemistry, and other fields of science and technology, Cauchy problems of hyperbolic equations arise that describe various processes. In the one-dimensional case, the system Carleman describes autocatalysis. A theorem on the stabilization of solutions of the Carleman system is formulated.