Blow-up phenomena and persistence property for the modified b-family of equations
Blow-up phenomena and persistence property for the modified b-family of equations
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DOI：
10.1016/j.jde.2016.09.027
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发表时间：
2017-02
影响因子：
2.4
通讯作者：
Ying Wang;Min Zhu
中科院分区：
文献类型：
--
作者：
Ying Wang;Min Zhu
本文研究了修正的B-族方程解的爆破机制和持久性。用具有不同参数的Riccati型微分不等式建立了爆破量沿特征线的动力学关系。该方法的主要特点是通过垂直移位来改进对溶液与其梯度的相对比率增长率的分析。此外，在加权空间中建立了解的持久性结果。
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.