In the first part of the paper it is shown, that in the case of specific initial conditions, solutions of the Cauchy problem for linearized Boltzmann equation have exponential damping when time tends to infinity. In the second part of the paper exact analytic solution of spatially homogeneous linearized Boltzmann equation is built by the use of discrete Laplace transform. The result may be useful in research tasks inside the area of applied rarefied gas dynamics.
Author: Firsov A.
ONE ALGORITHM FOR SOLVING THE INVERSE PROBLEM OF STABILITY OF A DYNAMICAL SYSTEM WITH UCERTAIN PARAMETERS AND ITS APPLICATION ON THE EXAMPLE OF PREDICTING THE COURSE OF CERTAIN PROCESSES IN CHEMICAL REACTORS
The task of estimating the ranges of permissible changes in the design parameters of a chemical reactor is solved in which the stability property of the monomerization process is retained in it. The solution is based on Ji-guang Sun’s results about the perturbation of the spectrum of the matrix, the elements of which depend on several indeterminate parameters.
NUMERICAL-ANALYTICAL METHOD FOR SOLVING THE INVERSE PROBLEM OF STABILITY FOR TECHNICAL SYSTEMS WITH MULTIPLE UNCERTAIN PARAMETERS
The paper considers the problem of determining the boundaries of possible changes of parameters of dynamic system whilst preserving stability of the system. The proposed method for determining such bounders is based on the research on the perturbation theory of matrix eigenvalues which depend on several perturbation parameters (by Ji-guang Sun). The results of this paper are based on the results presented by the authors at III TTOS Conference in May 2015.
ANALYTICAL ANALYSIS OF THE INVERSE STABILITY PROBLEM FOR SOME CLASSES OF NON-LINEAR DYNAMICAL SYSTEMS WITH A SMALL UNCERTAIN PARAMETER
In this paper we propose a method of solving inverse stability problem for some classes of non-linear dynamical systems with a small uncertain parameter. The method is based on T. Kato’s perturbation theory of linear operators. We illustrate our method by solving inverse stability problem in the situation of monomerization reaction inside the cascade of chemical reactors.
MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS
In the work a mathematical model for the non-stationary motion of liquid homogeneous viscous mixtures through pipelines is constructed. The corresponding integral equations expressing the laws of conservation of mass, momentum and energy are deriving, from which, in turn, we get the corresponding differential equations. The formulation of the initial and boundary conditions is given; the necessary additional relations that close the corresponding system of differential equations are indicated. A numerical algorithm for solving such a system is proposed. The corresponding numerical examples are given.