具有一般通量函数的双曲平衡律系统的BV熵解的结构

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2019-06-01 DOI:10.1142/S0219891619500139

F. Ancona, L. Caravenna, A. Marson

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引用次数: 0

摘要

本文描述了一类具有分段真非线性或线性退化特征场的一般严格双曲平衡律系统的BV熵解的定性结构。特别地，我们提供了一个精确的描述局部和全局波前结构的BV解由一个分数阶方案与波前跟踪算法相结合。这扩展了[S]中的相应结果。Bianchini和L. Yu，一维空间分段真正非线性严格双曲型守恒律的可容许BV解的整体结构[j] .微分方程学报，39(2)(2014):244-273。

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On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function

The paper describes the qualitative structure of BV entropy solutions of a general strictly hyperbolic system of balance laws with characteristic field either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an accurate description of the local and global wave-front structure of a BV solution generated by a fractional step scheme combined with a wave-front tracking algorithm. This extends the corresponding results in [S. Bianchini and L. Yu, Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension, Comm. Partial Differential Equations 39(2) (2014) 244–273] for strictly hyperbolic system of conservation laws.

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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.