Carleman类模型光滑解的整体存在及渐近分析

The Global Existence of Smooth Solution and Asymptotic Analysis of Carleman-type Model

讨论了带小参数的Carleman类宏观模型的解的一致先验估计,在此基础上获得了光滑解的整体存在性,证明了当小参数趋于零时,密度函数收敛于非线性扩散方程的解,并利用流函数讨论了相关的收敛速度.

The uniform priori estimate of the macroscopic equations of Carleman-type model with a small parameter are constructed.On the basis of priori estimate,we show the global existence of smooth solution.When the parameter tends to zero,the solution of Carleman-type model converges towards to the solution of the nonlinear diffusion equation.The rate of convergence is also obtained by Stream function.