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arXiv · 2204.12049

Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations

Erhan Bayraktar·Qi Feng·Wuchen Li
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Abstract

We study long-time dynamical behaviors of weakly self-consistent Vlasov-Fokker-Planck equations. We introduce Hessian matrix conditions on mean-field kernel functions, which characterizes the exponential convergence of solutions in $L^1$ distances. The matrix condition is derived from the dissipation of a selected Lyapunov functional, namely auxiliary Fisher information functional. We verify proposed matrix conditions in examples.

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Erhan Bayraktar, Qi Feng, Wuchen Li. 2022-04-26. Exponential Entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations. https://arxiv.org/abs/2204.12049

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