与非局部守恒定律有关的动力学方程的解

IF 0.5 4区 数学 Q4 MATHEMATICS, APPLIED
F. Berthelin
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引用次数: 0

摘要

众所周知,守恒定律是建模的重要组成部分。在许多模型中,考虑包括非本地流量的此类模型变得越来越重要。另一方面,动力学方程为通常的守恒定律提供了有趣的理论结果和数值格式。因此,研究与非局部流动守恒定律相关的动力学方程自然产生,并且非常重要。本文的目的是提出与维度上具有非局部通量的守恒定律相关的动力学模型[公式:见正文],并证明这些动力学方程解的存在性。这是第一个这样的结果。为了使论文尽可能具有一般性,我们强调了动力学模型必须验证的特性,以便应用本研究。因此,该结果可以应用于各种情况。我们给出了动力学模型的两组性质和两种不同的技术来获得存在性结果。最后,我们给出了我们的结果适用的动力学模型的两个例子,每组性质一个。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solutions of kinetic equations related to non-local conservation laws
Conservation laws are well known to be a crucial part of modeling. Considering such models with the inclusion of non-local flows is becoming increasingly important in many models. On the other hand, kinetic equations provide interesting theoretical results and numerical schemes for the usual conservation laws. Therefore, studying kinetic equations associated to conservation laws for non-local flows naturally arises and is very important. The aim of this paper is to propose kinetic models associated to conservation laws with a non-local flux in dimension [Formula: see text] and to prove the existence of solutions for these kinetic equations. This is the very first result of this kind. In order for the paper to be as general as possible, we have highlighted the properties that a kinetic model must verify in order that the present study applies. Thus, the result can be applied to various situations. We present two sets of properties on a kinetic model and two different techniques to obtain an existence result. Finally, we present two examples of kinetic model for which our results apply, one for each set of properties.
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来源期刊
Journal of Hyperbolic Differential Equations
Journal of Hyperbolic Differential Equations 数学-物理:数学物理
CiteScore
1.10
自引率
0.00%
发文量
15
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.
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