Ultra-analytic effect of Cauchy problem for a class of kinetic equations
Ultra-analytic effect of Cauchy problem for a class of kinetic equations
复制标题
DOI：
10.1016/j.jde.2009.01.028
复制
发表时间：
2009-03
期刊：
影响因子：
--
通讯作者：
Y. Morimoto;Chao-Jiang Xu
中科院分区：
文献类型：
--
作者：
Y. Morimoto;Chao-Jiang Xu
研究了一类动力学方程柯西问题的光滑化效应。我们首先考虑空间齐次的含Maxwell分子的非线性朗道方程和非齐次的线性Fokker-Planck方程，以显示Cauchy问题的超解析效应。这些光滑效果的结果是最佳的，类似于热方程。在第二部分中，我们研究了一类具有Maxwell分子的空间非齐次线性朗道方程模型，并给出了Cauchy问题的解析解。
The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous nonlinear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker–Planck equation to show the ultra-analytic effects of the Cauchy problem. Those smoothing effect results are optimal and similar to heat equation. In the second part, we study a model of spatially inhomogeneous linear Landau equation with Maxwellian molecules, and show the analytic effect of the Cauchy problem.