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Paper detail

Well-posedness results for superlinear Fokker-Planck equations

In this manuscript we deal with a class of nonlinear Fokker-Planck equations with the following structure \[ \partial_t u - ÷\big(M\nabla u+ E h(u)\big)=0, \] 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 $C([0,T),L^1)$ distributional solutions to initial-boundary value problems related to the equation above together with some qualitative properties of solutions.

preprint2026arXivOpen access
Stefano BuccheriFernando FarroniGabriella Zecca
math.AP
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Stefano BuccheriFernando FarroniGabriella Zecca

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