Conservation laws of mean field games equations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-07 DOI:10.1016/j.cnsns.2025.108796

Roman Kozlov

引用次数: 0

Abstract

Mean field games equations are examined for conservation laws. The system of mean field games equations consists of two partial differential equations: the Hamilton–Jacobi–Bellman equation for the value function and the forward Kolmogorov equation for the probability density. For separable Hamiltonians, this system has a variational structure, i.e., the equations of the system are Euler–Lagrange equations for some Lagrangian functions. Therefore, one can use the Noether theorem to derive the conservation laws using variational and divergence symmetries. In order to find such symmetries, we find symmetries of the PDE system and select variational and divergence ones. The paper considers separable, state-independent Hamiltonians in one-dimensional state space. It examines the most general form of the mean field games system for symmetries and conservation laws and identifies particular cases of the system which lead to additional symmetries and conservation laws.

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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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.