一类非齐次耦合弱退化抛物方程组的零可控性  

Null controllability of a class of nonhomogeneous coupled weakly degenerate parabolic equations

作　　者：杜润梅 陈博远 梅海婷 DU Runmei;CHEN Boyuan;MEI Haiting(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《长春工业大学学报》2022年第3期238-243,共6页Journal of Changchun University of Technology

基　　金：吉林省大学生创新创业计划项目(SS202110190055)。

摘　　要：研究一类非齐次耦合弱退化抛物方程组是否具有零可控性。由于原问题的零可控性等价于对偶问题的可观测性,所以主要研究它的对偶问题。首先,介绍单个方程解的适定性,Carleman估计;其次,利用单个方程的Carleman估计得出耦合方程组的Carleman估计,进而得出对偶问题的可观测性。The null controllability of nonhomogeneous coupled weakly degenerate parabolic equations is studied.Since the null controllability of the primal problem is equivalent to the observability of the dual problem,its dual problem is mainly investigated.Firstly,we introduce the well-posedness of the solution and Carleman estimate for the single equation.Next,we obtain the Carleman estimates of the coupled equations by the Carleman estimate of the single equation.Further,we get the observability of the coupled system.

关 键 词：非齐次 弱退化 抛物方程组 零可控性 Carleman估计 

分 类 号：O175.26[理学—数学]