APPLICATION OF THE METHOD OF DIFFERENTIAL CONSTRAINTS TO SYSTEMS OF EQUATIONS WRITTEN IN RIEMANN INVARIANTS

Solutions of one-dimensional equations of gas dynamics and the equations describing the behavior of a nonlinear elastic material are reduced to solving a system of homogeneous differential equations written in Riemann invariants. It is shown that the solution of the Cauchy problem for such a system...

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Bibliographic Details
Published in:	Journal of applied mechanics and technical physics Vol. 62; no. 3; pp. 351 - 360
Main Authors:	Meleshko, S. V., Shultz, E.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-05-2021 Springer Nature B.V
Subjects:	Applications of Mathematics Cauchy problems Classical and Continuum Physics Classical Mechanics Differential equations Fluid- and Aerodynamics Gas dynamics Invariants Mathematical analysis Mathematical Modeling and Industrial Mathematics Mechanical Engineering Ordinary differential equations Physics Physics and Astronomy gas dynamics equations equations of nonlinear elasticity method of differential constraints Riemann invariants
Online Access:	Get full text
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Summary:	Solutions of one-dimensional equations of gas dynamics and the equations describing the behavior of a nonlinear elastic material are reduced to solving a system of homogeneous differential equations written in Riemann invariants. It is shown that the solution of the Cauchy problem for such a system allowing for a differential constraint is reduced to solving a system of ordinary differential equations. Examples of solutions for certain initial data are given.
ISSN:	0021-8944 1573-8620
DOI:	10.1134/S0021894421030019