Lp Contractive solutions for scalar conservation laws

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2022-06-01 DOI:10.1142/s0219891622500059

Kihito Hinohara, Natsuki Minagawa, Hiroki Ohwa, Hiroya Suzuki, Shou Ukita

引用次数: 1

Abstract

We estimate the [Formula: see text] distance between piecewise constant solutions to the Cauchy problem of scalar conservation laws and propose a sufficient condition for having an [Formula: see text] contraction of such solutions. Moreover, we prove that there exist [Formula: see text] contractive solutions on a set of all monotone bounded initial functions to the Cauchy problem of scalar conservation laws with convex or concave flux functions.

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标量守恒定律的Lp压缩解

我们估计了标量守恒定律Cauchy问题的分段常数解之间的[公式：见正文]距离，并提出了此类解具有[公式：参见正文]收缩的充分条件。此外，我们证明了具有凸或凹通量函数的标量守恒定律的Cauchy问题在一组全单调有界初始函数上存在[公式：见正文]压缩解。

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.