空间非均匀线性Boltzmann方程在硬势情形下解的最优指数收敛速率

Optimal Exponential Decay for the Linear Inhomogeneous Boltzmann Equation with Hard Potentials

该文研究空间非均匀线性Boltzmann方程在周期区域上非角截断硬势情形下解的渐近行为.在带有多项式权的L_(v)^(1)L_(x)^(2)(<v>^(k))空间中得到了解的最优指数收敛速率.将从谱理论和半群理论的角度来对该方程进行分析,主要方法是借助于在Hilbert空间中的强制性估计、算子分解以及空间拉大理论等.

In this paper,we consider the asymptotic behavior of solutions to the linear spatially inhomogeneous Boltzmann equation for hard potentials in the torus.We obtain an optimal rate of exponential convergence towards equilibrium in a Lebesgue space with polynomial weight L_(v)^(1)L_(x)^(2)(<v>^(k)).This model is analyzed from a spectral point of view and from the point of view of semigroups.Our strategy is taking advantage of the spectral gap estimate in the Hilbert space with inverse Gaussian weight,the factorization argument and the enlargement method.