演講訊息 TALKS

摘要 We study the equilibrating effects of the boundary and intermolecular collision for rarefied gases in the spherical domain with variable boundary temperature in $\mathbb{R}^d$, $d=1,2,$ under the Maxwell-type boundary condition. First, we obtain the algebraic convergence rate to the steady state for free molecular flow. And then we construct the steady state solution of the Boltzmann equation for large Knudsen numbers and small variation of boundary temperature. We establish the nonlinear stability, with exponential rate of the stationary Boltzmann solutions. The results hold for the models of Maxwell molecule, hard potential, and hard sphere. Our analysis is based on the explicit formulations of boundary condition for symmetric domain.