Differential constraints for hyperbolic systems through k-Riemann invariants

TL;DR

This paper introduces a reduction method using k-Riemann invariants within differential constraints to find exact wave solutions for nonhomogeneous hyperbolic systems, enabling the solution of Riemann problems.

Contribution

It develops a novel reduction procedure leveraging k-Riemann invariants for hyperbolic systems with nonhomogeneous terms, expanding solution techniques.

Findings

Exact wave solutions for nonhomogeneous hyperbolic systems derived

Characterization of rarefaction waves in nonhomogeneous models achieved

Application demonstrated on Euler system with source term

Abstract

In this paper we develop a reduction procedure for determining exact wave solutions of first order quasilinear hyperbolic one-dimensional nonhomogeneous systems. The approach is formulated within the theoretical framework of the method of differential constraints and it makes use of the $k-$Riemann invariants. The solutions obtained permit to characterize rarefaction waves also for nonhomogeneous models so that Riemann problems can be solved. Applications to the Euler system describing an ideal fluid with a source term are given.