Application of the Method of Differential Constraints to Systems of Equations Written in Riemann Invariants
S. V. Meleshko, E. Shul'tz
Mathematical College, Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand
Keywords: method of differential constraints, Riemann invariants, gas dynamics equations, equations of nonlinear elasticity
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.
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