Isotropic hypoellipticity and trend to the equilibrium for the Fokker-Planck equation with high degree potential

Numerical Studies and Simulation of the Lower Hybrid Waves Current Drive by using Fokker – Planck Equation in NSST and HT-7 Tokamaks

Recent experiments on the spherical tokamak have discovered the conditions to create a powerful plasma and ensure easy shaping and amplification of stability, high bootstrap current and confinement energy. The spherical tours (ST) fusion energy development path is complementary to the tokamak burning plasma experiment such as NSTX and higher toroidal beta regimes and improves the design of a po...

Pseudo-spectral ‎M‎atrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

Iterative methods for solving non linear Fokker-Planck equation

Conservative and entropy numerical scheme for the isotropic Fokker-Planck-Landau equation

Homogeneous Fokker-Planck-Landau equation is investigated for coulombian potential and isotropic distribution function i.e. when the distribution function depends only on time and on the modulus of the velocity. We derive a new conservative and entropy decaying semi-discretized Landau equation for which we prove the existence of global in time positive solutions. For the time-discretized equati...

On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems : The linear Fokker-Planck equation

We study the long-time behavior of kinetic equations in which transport and spatial confinement (in an exterior potential, or in a box) are associated with a (degenerate) collision operator, acting only in the velocity variable. We expose a general method, based on logarithmic Sobolev inequalities and the entropy, to overcome the well-known problem, due to the degeneracy in the position variabl...