Asymptotic behavior of Riemann solutions for the one-dimensional mean-field games in conservative form with the logarithmic coupling term

IF 2.8 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics Pub Date : 2024-07-15 DOI:10.1016/j.ijnonlinmec.2024.104837

Meina Sun, Chenjia Wang

引用次数: 0

Abstract

Construction of Riemann solutions for a hyperbolic system in conservative form arising from the one-dimensional mean-field games with the quadratic Hamiltonian and the logarithmic coupling term are provided in detail. Moreover, the delta shock formation is concretely analyzed from the limit of double-shock-solution as well as the emergence of vacuum state is also specifically discussed from the limit of double-rarefaction-solution when the coupling coefficient drops to zero. Accordingly, the remarkable cavitation and concentration phenomena can be closely observed and explored. Additionally, the numerical experiments are also presented in correspondence to authenticate the theoretical analysis results.

查看原文本刊更多论文

带有对数耦合项的保守形式一维均场博弈黎曼解的渐近行为

详细介绍了由具有二次哈密顿和对数耦合项的一维均场博弈产生的保守形式双曲系统的黎曼解的构造。此外，还从双冲击解的极限具体分析了三角冲击的形成，并具体讨论了当耦合系数降为零时，真空状态的出现。因此，可以仔细观察和探索显著的空化和浓缩现象。此外，还给出了相应的数值实验来验证理论分析结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal of Non-Linear Mechanics 物理-力学

CiteScore

5.50

自引率

9.40%

发文量

192

审稿时长

67 days

期刊介绍： The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.