双曲型系统的k−Riemann不变量微分约束

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-28 DOI:10.1016/j.cnsns.2025.109379

Alessandra Jannelli , Natale Manganaro , Alessandra Rizzo

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引用次数: 0

摘要

本文给出了确定一阶拟线性双曲型一维非齐次系统精确波解的约简方法。该方法是在微分约束方法的理论框架内制定的，它利用了k−黎曼不变量。所得到的解也允许对非均匀模型的稀疏波进行表征，从而可以解决黎曼问题。给出了用源项描述理想流体的欧拉系统的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Differential constraints for hyperbolic systems through k−Riemann invariants

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.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.