Abstract

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.

中文翻译：

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微分约束法在用黎曼不变量写成的方程组中的应用

摘要

气体动力学的一维方程和描述非线性弹性材料行为的方程的解被简化为求解用黎曼不变量编写的齐次微分方程组。结果表明，对于这种允许微分约束的系统，柯西问题的解被简化为求解常微分方程组。给出了某些初始数据的解决方案示例。