Semi-linear parabolic equations on homogenous Lie groups arising from mean field games
Semi-linear parabolic equations on homogenous Lie groups arising from mean field games
Abstract The existence and the uniqueness of solutions to some semilinear parabolic equations on homogeneous Lie groups, namely, the Fokker–Planck equation and the Hamilton–Jacobi equation, are addressed. The anisotropic geometry of the state space plays a crucial role in our analysis and creates several issues that need to be overcome. …