Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient
Catastrophe

A. V. Aksenov; Аксенов А. В.; K. P. Druzhkov; Дружков К. П.

doi:10.31857/S0568528122600734

Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient Catastrophe

Authors: Aksenov A.V.¹^,2, Druzhkov K.P.¹^,3
Affiliations:
1. Moscow State University
2. National Research Nuclear University MEPh
3. Moscow Institute of Physics and Technology (State University)
Issue: No 1 (2023)
Pages: 135-143
Section: Articles
URL: https://journals.rcsi.science/1024-7084/article/view/135058
DOI: https://doi.org/10.31857/S0568528122600734
EDN: https://elibrary.ru/AJZXYK
ID: 135058

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract
About the authors
References
Supplementary files
Statistics

Abstract

The system of equations that describes one-dimensional polytropic gas flows is considered. The invariants up to the second order of characteristics of the considered system of equations are classified. The method of reducing the Cauchy problems to systems of ordinary differential equations is proposed. Examples of the solutions without gradient catastrophe are constructed using invariants of characteristics supplementary to the Riemann invariants.

Keywords

gas dynamics, Riemann invariants, invariants of characteristics, gradient catastrophe, exact solutions

About the authors

A. V. Aksenov

Moscow State University; National Research Nuclear University MEPh

Email: aksenov@mech.math.msu.su
Moscow, Russia; Moscow, Russia

K. P. Druzhkov

Moscow State University; Moscow Institute of Physics and Technology (State University)

Author for correspondence.
Email: konstantin.druzhkov@gmail.com
Moscow, Russia; Dolgopudnyi, Moscow oblast, Russia

References

Riemann B. Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite // Aus dem achten Bande der Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematischphysikalische Klasse. 1860. Band 8. Nr. 43. S. 43–66. [Retrieved from https://eudml.org/doc/135717]
Darboux M.G. Sur la théorie des équations aux dérivées partielles du second ordre // Comptes rendus hebdomadaires des sкnces de l’Académie des sciences Paris. 1870. V. 70. P. 675–678.
Darboux M.G. Sur la théorie des équations aux dérivées partielles // Comptes rendus hebdomadaires des séances de l’Académie des sciences Paris. 1870. V. 70. P. 746–749.
Goursat M.E. Leçons sur l’intégration des équations aux deréeves partielles du second order a deux variables indépendantes. Tome II. Paris. 1898. 174 p. (Librairie scientifique A. Hermann)
Капцов О.В. Методы интегрирования уравнений с частными производными. М.: ФИЗМАТЛИТ, 2009. 184 с.
Аксенов А.В. Нелинейные периодические волны в газе // Изв. РАН. МЖГ. 2012. № 5. С. 88–98.
Рождественский Б.Л., Яненко Н.Н. Системы квазилинейных уравнений и их приложения к газовой динамике, М.: Наука. Главная редакция физико-математической литературы, 1978. 687 с.
Aksenov A.V., Druzhkov K.P., Kaptsov O.V. Application of invariants of characteristics to construction of solutions without gradient catastrophe // International Journal of Non-Linear Mechanics. 2022. V. 147. № 104249. P. 1–8.