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The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation [PDF]
Indiana University Mathematics Journal, 2019 One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+\mathrm{ div}(D(x)b(u)u)=0, \ t\ge0, \ x\in\mathbb{R}^d,\hspace{1cm} (1)$$ and under appropriate hypotheses on $\beta,$ $D$ and $b ...
V. Barbu, M. Rockner
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Journal of Function Spaces, 2021 The main purpose of this paper is to apply the Lie symmetry analysis method for the two-dimensional time fractional Fokker-Planck (FP) equation in the sense of Riemann–Liouville fractional derivative.
Nisrine Maarouf, Khalid Hilal
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The kinetic Fokker-Planck equation with mean field interaction [PDF]
Journal des Mathématiques Pures et Appliquées, 2019 We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation.
A. Guillin +3 more
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Advances in Difference Equations, 2020 This paper provides a numerical approach for solving the time-fractional Fokker–Planck equation (FFPE). The authors use the shifted Chebyshev collocation method and the finite difference method (FDM) to present the fractional Fokker–Planck equation into ...
Haile Habenom, D. L. Suthar
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Radiative Transfer Limits of Two-Frequency Wigner Distribution for Random Parabolic Waves [PDF]
, 2006 The present note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a ...
Albert C. Fannjiang +11 more
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Efficient statistically accurate algorithms for the Fokker-Planck equation in large dimensions [PDF]
Journal of Computational Physics, 2017 Solving the Fokker–Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing the fat tailed ...
N. Chen, A. Majda
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Interval Wavelet Numerical Method on Fokker-Planck Equations for Nonlinear Random System
Advances in Mathematical Physics, 2013 The Fokker-Planck-Kolmogorov (FPK) equation governs the probability density function (p.d.f.) of the dynamic response of a particular class of linear or nonlinear system to random excitation.
Li-wei Liu
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
Entropy, 2018 We study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to
Piotr Weber +3 more
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Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems [PDF]
, 2002 The master equation approach to Lyapunov spectra for many-particle systems is applied to non-equilibrium thermostatted systems to discuss the conjugate pairing rule. We consider iso-kinetic thermostatted systems with a shear flow sustained by an external
C. Wagner +43 more
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Mean-field approximation of counting processes from a differential equation perspective
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Deterministic limit of a class of continuous time Markov chains is considered based purely on differential equation techniques. Starting from the linear system of master equations, ordinary differential equations for the moments and a partial ...
Dávid Kunszenti-Kovács, Péter Simon
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