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DATE | 2020-04-21 14:10-15:00 |

PLACE | 數學館3174教室 |

SPEAKER | 林育竹 副教授（成功大學數學系） |

TITLE | The Pointwise Estimate of Some Kinetic Equations |

ABSTRACT | In this talk I will talk about my recent work in the kinetic theory. In the whole space, the Boltzmann equations for hard and soft potentials, the Landau equation for two species and the Fokker-Planck equation are included, and the wave-remainder decomposition, the regularization estimate, the weighted energy estimate, and the compensating function method play a crucial role in the argument. In these articles, we reveal the space-time structure of solutions to the linearized equations. For the boundary-value problem, I will talk about the Milne problem for a binary gas mixture, which is a joint work with Professors Kazuo Aoki and Kung-Chien Wu. The existence and uniqueness of the solutions are proved, and the accurate asymptotic behavior in the far field is obtained. In particular, the precise rate of approach of the solution to the state at infinity is expressed in terms of the decay rate in the molecular velocity of the boundary data for both species. |