Well-posedness results for superlinear Fokker-Planck equations
Abstract
In this manuscript we deal with a class of nonlinear Fokker-Planck equations with the following structure \[ ∂t u - (M∇ u+ E h(u))=0, \] with M a bounded elliptic matrix, E a vector field in a suitable Lebesgue space, and h(u) featuring a superlinear growth for u large. We provide existence results of C([0,T),L1) distributional solutions to initial-boundary value problems related to the equation above together with some qualitative properties of solutions.
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