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

作　　者：陆小菲 林春进 LU Xiao-fei;LIN Chun-jin(College of Science,Hohai University,Nanjing 211100,China)

机构地区：[1]河海大学理学院,江苏南京211100

出　　处：《云南师范大学学报（自然科学版）》2019年第1期36-42,共7页Journal of Yunnan Normal University:Natural Sciences Edition

基　　金：国家自然科学基金资助项目(11201116)

摘　　要：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.

关 键 词：能量估计 整体光滑解 收敛速度 

分 类 号：O175.27[理学—数学]