Blow-up phenomena and persistence property for the modified b-family of equations

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• 作者：Ying Wang^a ; ^{nadine_1979@163.com} ; Min Zhu^b ; ^{zhumin@njfu.com}
• 关键词：35G25 ; 35B44 ; 35Q35
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：1161-1191
• 全文大小：393 K
• 卷排序：262

文摘

In this paper, we study the blow-up mechanism and persistence property of solutions to the modified b-family of equations. The dynamics of the blow-up quantity along the characteristics is established by the Riccati-type differential inequality with various parameters. The key feature of the method is to refine the analysis on the growth rate of the relative ratio between solution and its gradient by performing a vertical shift. Furthermore, the persistence results for the solution are established in weighted spaces.