scholarly journals The analysis of gas dynamics equations with initial and boundary conditions and the construction of the corresponding averaged system

2013 ◽  
Vol 54 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Rima Kriauzienė
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Hyperbolic System ◽  
Gas Dynamics ◽  
System Of Differential Equations ◽  
Gas Dynamics Equations ◽  
Large Domain ◽  
First Order ◽  
Initial And Boundary Conditions ◽  
Asymptotical Analysis

In this paper hyperbolic system of the first order gas dynamics PDE with initial and boundary conditions is studied. The aim of the paper is to construct the averaged system of differential equations in order to find the uniformly valid in a large domain asymptotical solution. The averaged system is a new object of asymptotical analysis.

Modeling of the Process of Drying and Coalescing Nanodispersion Spreading

2021 ◽  
Vol 887 ◽  
pp. 557-563
Author(s):  
D.M. Mordasov ◽  
M.D. Mordasov
Keyword(s):  
Contact Angle ◽  
Differential Equations ◽  
Mathematical Description ◽  
Transition Function ◽  
System Of Differential Equations ◽  
Theoretical Justification ◽  
Spreading Process ◽  
Optimal Amount ◽  
First Order ◽  
Energy Processes

The spreading process of drying and coalescing nanodispersion was simulated using the method of analogies. A mathematical description of the energy processes in the proposed physical model was obtained in the form of a system of differential equations of the first order. A transition function that describes the dynamics of the change in the contact angle when the nanodispersion drop spreads was obtained as a result of solving the system of differential equations. The physical meaning of the transition function coefficients was established. Based on the analysis of the ratio of the transition function coefficients, a theoretical justification for the results of experiments on choosing the optimal amount of desiccant introduced into styrene-acrylic nanodispersion was given.

ASYMPTOTICAL ANALYSIS OF ONE DIMENSIONAL GAS DYNAMICS EQUATIONS

2001 ◽  
Vol 6 (1) ◽  
pp. 117-128 ◽  
Author(s):  
A. Krylovas ◽  
R. Čiegis
Keyword(s):  
Gas Dynamics ◽  
Numerical Experiments ◽  
Method Of Averaging ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Resonance Case ◽  
Gas Dynamics Equations ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Asymptotical Analysis

A method of averaging is developed for constructing a uniformly valid asymptotic solution for weakly nonlinear one dimensional gas dynamics systems. Using this method we give the averaged system, which disintegrates into independent equations for the non‐resonance systems. Conditions of the resonance for periodic and almost periodic solutions are presented. In the resonance case the averaged system is solved numerically. Some results of numerical experiments are given.

A first order system of differential equations for covariant σ models

1979 ◽  
Vol 20 (12) ◽  
pp. 2619-2620
Author(s):  
C. Reina ◽  
M. Martellini ◽  
P. Sodano
Keyword(s):  
Differential Equations ◽  
Order System ◽  
System Of Differential Equations ◽  
First Order

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

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