The Cauchy problem for the BGK equation with an external force

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• 作者：Jinbo Wei ; ^{jinbo_wei@163.com} ; Xianwen Zhang ^{xwzhang@mail.hust.edu.cn}
• 关键词：BGK equation ; External force ; L1 solution ; Lp solution
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：1 July, 2012
• 年：2012
• 卷：391
• 期：1
• 页码：10-25
• 全文大小：237 K

文摘

In this paper, we study the Cauchy problem for the BGK equation with an external force. Firstly, we establish an existence result for this equation, and obtain some weighted estimates. Then, by means of the regularizing effects to the initial datum, we construct the approximate solutions and obtain some uniform estimates of the approximate solutions. Finally by using compactness method and passing to the limit, we prove the existence theorems of the and solutions and establish the propagation properties of the moments.