1,872 research outputs found
Conservation laws arising in the study of forward-forward Mean-Field Games
We consider forward-forward Mean Field Game (MFG) models that arise in
numerical approximations of stationary MFGs. First, we establish a link between
these models and a class of hyperbolic conservation laws as well as certain
nonlinear wave equations. Second, we investigate existence and long-time
behavior of solutions for such models
Obstacle Mean-Field Game Problem
In this paper, we introduce and study a first-order mean-field game obstacle
problem. We examine the case of local dependence on the measure under
assumptions that include both the logarithmic case and power-like
nonlinearities. Since the obstacle operator is not differentiable, the
equations for first-order mean field game problems have to be discussed
carefully. Hence, we begin by considering a penalized problem. We prove this
problem admits a unique solution satisfying uniform bounds. These bounds serve
to pass to the limit in the penalized problem and to characterize the limiting
equations. Finally, we prove uniqueness of solutions
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