Nonlinear Fokker-Planck Equations

By T. Frank. 2005

256 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/07a047a32ea66ac9d2f998ea11b40bbd50e94df5

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In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Rational Forecasts or Social Opinion Dynamics? Identification of Interaction Effects in a Business Climate Survey (2009, background): “The Fokker-Planck equation associated to a stochastic process is a parabolic partial differential equation that occupies a very prominent place in statistical physics (Risken, 1989; Frank, 2005).”
Nonlinear mobility continuity equations and generalized displacement convexity (2009, background): “A new class of “dynamical” distances In a number of problems from mathematical biology [8,9,14,17,18,26,27,36] mainly in chemotaxis with prevention of overcrowding, mathematical physics [10,13,21,22,28,29,40], studies of phase segregation [23,39], and studies of thin liquid films [6], the mobility o”
Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations (2007, unknown): “omenologicallyadynamicalmodelbywritingthe evolution of the density as a continuity equation ∂tρ= −∇·J where the current is proportional to the gradient of the functional derivative of the free energy [36], i.e. ∂ρ ∂t = ∇ · χ(r,t)ρ∇ δF δρ . (53) For the free energy (36), we have δF δρ = TC′(ρ) +Φ, ”
From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE (2018, methodology): “ase where the solutions µt, t≥ 0, to (1.2) have densities with respect to the Lebesgue measure dx, i.e., µt(dx) = u(t,x)dx,t≥ 0, (1.2) can be rewritten (in the sense of Schwartz distributions) as (cf.[16]) (1.5) ∂ ∂t u(t,x) = 1 2 Xd i,j=1 ∂2 ∂xi∂xj [aij(t,x,u(t,·)dx)u(t,x)] − Xd i=1 ∂ ∂xi [bi(t,x,u(”