On a global integral equation arising in the discretization of granular flows

IF 1.3 2区数学 Q1 MATHEMATICS

Nonlinear Analysis-Theory Methods & Applications Pub Date : 2025-06-20 DOI:10.1016/j.na.2025.113871

Adrian Tudorascu

引用次数: 0

Abstract

We construct approximations to the solution for the homogeneous nonlinear friction equation with generic initial data by time-discretizing the fow in the Wasserstein space.The associated Euler-Lagrange equation for the optimal map is a global integral equation which we analyze in detail. It is remarkable that the solution is explicit up to its

L^{2}

-norm. An estimate of the long time behavior of the support of the solution to the original PDE arises as a consequence

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粒流离散化中出现的一个全局积分方程

通过对Wasserstein空间中的流动进行时间离散，构造了具有一般初始数据的齐次非线性摩擦方程的近似解。最优映射的相关欧拉-拉格朗日方程是一个全局积分方程，我们对此进行了详细的分析。值得注意的是，解是显式的，直到它的L2范数。因此，需要对原始PDE解决方案的支持的长期行为进行估计

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

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.