The role of a strong confining potential in a nonlinear Fokker-Planck equation
The paper studies the connection between a class of nonlinear and nonlocal Fokker-Planck equation defined on a bounded domain with no-flux boundary condition with the the Cauchy problem of the same euqation but with a strong confinement potential. The authors show that the the solution of the problem can be obtained as the weak limit of the solution of the Cauchy problem as the confinement parameter tends to infinity. The proof relies on some uniform \(L^2\)-energy estimates and free energy estimates for nondegenerate and degenerate equations.
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