Shadow wave solutions for a scalar two-flux conservation law with Rankine–Hugoniot deficit

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2021-05-29 DOI:10.1142/s021989162150017x

Tanja Kruni'c, M. Nedeljkov

引用次数: 0

Abstract

This paper deals with hyperbolic conservation laws exhibiting a flux discontinuity at the origin and which does not admit a weak solution satisfying the Rankine–Hugoniot jump condition. We therefore seek unbounded solutions in the form of shadow waves supported by at the origin. The shadow waves are defined as nets of piecewise constant functions approximating a shock wave to which we add a delta function and possibly another unbounded part.

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具有Rankine–Hugoniot亏差的标量双通量守恒定律的影子波解

本文讨论了在原点处具有通量不连续且不存在弱解的双曲守恒律，该双曲守恒律满足Rankine-Hugoniot跳跃条件。因此，我们寻求由原点支持的阴影波形式的无界解。阴影波被定义为近似激波的分段常数函数网，我们在其中加入一个δ函数，可能还有另一个无界部分。

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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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.