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On One Inverse Problem for the Kolmogorov–Fokker–Planck Equation
AbstractA mathematical description of the household economic behavior with the help of the Kolmogorov–Fokker–Planck equation is studied. This...
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Potential stability of the Fokker–Planck equation
We consider the kinetic Fokker–Planck equations with either a confining potential or a friction potential in the whole space. We prove that the...
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Controlling a Nonlinear Fokker–Planck Equation via Inputs with Nonlocal Action
This paper concerns an optimal control problem ( P ) associated to a nonlinear Fokker–Planck equation via inputs with nonlocal action. The...
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On Solutions of the Fokker–Planck Equations
In this paper, we find necessary and sufficient conditions for existence of a transformation of independent spatial variables that transforms the...
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Lie symmetry analysis and some new exact solutions of the Fokker–Planck equation
The classical symmetry method is often employed to find precise solutions to differential equations. This method has yielded several new symmetry...
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Some Computational Methods for the Fokker–Planck Equation
Three computational techniques are proposed for the numerical solution of the Fokker–Planck equation (FPE): the semi-implicit Euler, implicit Euler,...
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Calculation of Plasma Heating by Charged Products of Thermonuclear Reactions Based on the Simplified Fokker–Planck Equation
AbstractA two-level time scheme for solving the simplified Fokker–Planck kinetic equation is created as applied to the transport of charged products...
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Fokker–Planck–Kolmogorov Equations with a Parameter
AbstractFor Fokker–Planck–Kolmogorov equations with coefficients depending measurably on a parameter we prove the existence of solutions that are...
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Time Dependent Fokker–Planck Equations
In this chapter, the existence of strong solutions to time-dependent nonlinear Fokker-Planck equations is studied.
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Geometric thermodynamics for the Fokker–Planck equation: stochastic thermodynamic links between information geometry and optimal transport
We propose a geometric theory of non-equilibrium thermodynamics, namely geometric thermodynamics, using our recent developments of...
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Convergence to Equilibrium of Nonlinear Fokker–Planck Flows
It is studied the asymptotic behaviour and convergence to equilibrium states of solutions to nonlinear Fokker-Planck equations (the H-theorem). The...
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Markov Processes Associated with Nonlinear Fokker–Planck Equations
In this chapter, one presents an introductory treatment on McKean-Vlasov stochastic differential equations and their relationship with Fokker-Planck...
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Pointwise and weighted Hessian estimates for Kolmogorov–Fokker–Planck-type operators
In this article, we obtain Hessian estimates for Kolmogorov–Fokker–Planck operators in non-divergence form in several Banach function spaces. Our...
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Existence of Nonlinear Fokker–Planck Flows
This chapter presents the core of existence and uniqueness theory for mild and distributional solutions to the Cauchy problem for nonlinear...
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On nonlocal Fokker–Planck equations with nonlinear force fields and perturbations
We deal with a class of nonlocal Fokker–Planck equations subject to nonlinear force fields and perturbations, where the questions of global...
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Structure Preserving Schemes for Fokker–Planck Equations of Irreversible Processes
In this paper, we construct structure preserving schemes for solving Fokker–Planck equations associated with irreversible processes. The proposed...
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Numerical Approximations for the Fractional Fokker–Planck Equation with Two-Scale Diffusion
Fractional Fokker–Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing numerical...
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Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations
We study long-time dynamical behaviors of weakly self-consistent Vlasov–Fokker–Planck equations. We introduce Hessian matrix conditions on mean-field...