Solutions for nonlinear Fokker-Planck equations with measures as initial data and Mckean-Vlasov equations

DOI10.1016/j.jfa.2021.108926zbMath1458.35415arXiv2005.02311OpenAlexW3122969257MaRDI QIDQ2225264

Viorel Barbu, Michael Roeckner

Publication date: 5 February 2021

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.02311

zbMATH Keywords

Fokker-Planck equation\(m\)-accretiveMcKean-Vlasov stochastic differential equationmeasure as initial data

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Asymptotic behavior of solutions to PDEs (35B40) Fokker-Planck equations (35Q84)

Related Items (18)

Nonlinear Fokker-Planck equation with reflecting boundary conditions ⋮ Distribution-dependent stochastic porous media equations ⋮ Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients ⋮ Flow selections for (nonlinear) Fokker-Planck-Kolmogorov equations ⋮ Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: the degenerate case ⋮ Well-posedness of density dependent SDE driven by \(\alpha \)-stable process with Hölder drifts ⋮ Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift ⋮ Existence of Optimal Control for Nonlinear Fokker–Planck Equations in \(\boldsymbol{L^1(\mathbb{R}^d)}\). ⋮ Stochastic Fokker–Planck Equations for Conditional McKean–Vlasov Jump Diffusions and Applications to Optimal Control ⋮ Exact Controllability of Fokker–Planck Equations and McKean–Vlasov SDEs ⋮ Strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type ⋮ Controlling a generalized Fokker-Planck equation via inputs with nonlocal action ⋮ Euler scheme for density dependent stochastic differential equations ⋮ Existence and uniqueness of solution to the two-phase Stefan problem with convection ⋮ Large deviation principle for McKean-Vlasov quasilinear stochastic evolution equations ⋮ Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs ⋮ The invariance principle for nonlinear Fokker-Planck equations ⋮ The Trotter product formula for nonlinear Fokker-Planck flows

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