Abstract
We study linear two-and-a-half-dimensional Vlasov equations under the logarithmic gravity potential in the half-space of diffuse reflection boundary. We prove decay-in-time of the exponential moments with a polynomial rate, which depends on the base logarithm.
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References
Aoki, K., Golse, F.: On the speed of approach to equilibrium for a collisionless gas. Kinet. Relat. Models 4(1), 87–107 (2011)
Bernou, A.: A semigroup approach to the convergence rate of a collisionless gas. Kinet. Relat. Models 13(6), 1071–1106 (2020)
Cañizo, A.J., Mischler, S.: Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups. J. Funct. Anal. 284(7), 109830 (2023)
Jin, J., Kim, C.: Damping of kinetic transport equation with diffuse boundary condition. SIAM J. Math. Anal. 54(5), 5524–5550 (2022)
Jin, J., Kim, C.: Exponential Mixing of Vlasov equations under the effect of gravity and boundary. J. Differ. Equ. 366, 644 (2023)
Kim, C.: Nonlinear asymptotic stability of inhomogeneous steady solutions to boundary problems of Vlasov–Poisson equation. arXiv:2210.00677
Lods, B., Mokhtar-Kharroubi, M., Rudnicki, R.: Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators. Ann. Inst. H. Poincare Anal. Non Lineaire 37(4), 877–923 (2020)
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This project is partly supported by NSF-CAREER 2047681, Brain Pool fellowship, and Simons fellowship.
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Jin, J., Kim, C. Boundary Effect Under 2D Newtonian Gravity Potential in the Phase Space. La Matematica (2024). https://doi.org/10.1007/s44007-024-00097-y
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DOI: https://doi.org/10.1007/s44007-024-00097-y