Deterministic mean field games with control on the acceleration

DOI10.1007/s00030-020-00634-yzbMath1442.35463arXiv1908.03330OpenAlexW3025729845MaRDI QIDQ2189997

Claudio Marchi, Paola Mannucci, Yves Achdou, Nicoletta Tchou

Publication date: 17 June 2020

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.03330

zbMATH Keywords

first-order Hamilton-Jacobi equationsmean field gamesdouble integratornon-coercive Hamiltonian

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Weak solutions to PDEs (35D30) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Viscosity solutions to PDEs (35D40) Systems of nonlinear first-order PDEs (35F50) Mean field games (aspects of game theory) (91A16)

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A variational approach to first order kinetic mean field games with local couplings ⋮ Deterministic Mean Field Games with Control on the Acceleration and State Constraints ⋮ Non-coercive first order mean field games ⋮ Generic properties of first-order mean field games ⋮ Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System ⋮ A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications ⋮ A singular perturbation problem for mean field games of acceleration: application to mean field games of control ⋮ Convergence of some mean field games systems to aggregation and flocking models ⋮ A Cucker--Smale Inspired Deterministic Mean Field Game with Velocity Interactions ⋮ Mild and weak solutions of Mean Field Games problem for linear control systems ⋮ Non coercive unbounded first order mean field games: the Heisenberg example

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