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 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.
Jannelli, A., Manganaro, N., Rizzo, A. (2026). Differential constraints for hyperbolic systems through k−Riemann invariants. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION, 152 [10.1016/j.cnsns.2025.109379].
Differential constraints for hyperbolic systems through k−Riemann invariants
Natale Manganaro
;Alessandra Rizzo
2026-01-01
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 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.
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