Electron. J. Differential Equations, Vol. 2019 (2019), No. 123, pp. 1-15.

Null controllability of nonlinear control systems governed by coupled degenerate parabolic equations

Fengdan Xu, Jingxue Yin, Mingjun Zhou, Qian Zhou

Abstract:
This article concerns the null controllability of a nonlinear control system governed by coupled degenerate parabolic equations. We first establish the Carleman estimate and the observability inequality for solutions to the conjugate problem. Then we can prove the observability inequality and the null controllability of the linear control system. Finally, the nonlinear control system is shown to be null controllable by a fixed point argument and compact estimates.

Submitted November 11, 2018. Published November 21, 2019.
Math Subject Classifications: 93B05, 93C20, 35K65.
Key Words: Null controllability; coupled degenerate parabolic equations; Carleman estimate.

Show me the PDF file (331 KB), TEX file for this article.

Fengdan Xu
School of Mathematics
Jilin University
Changchun 130012, China
email: 245952950@qq.com
Jingxue Yin
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: yjx@scnu.edu.cn
Mingjun Zhou
School of Mathematics
Jilin University
Changchun 130012, China
email: zhoumingjun@jlu.edu.cn
Qian Zhou
School of Mathematics
Jilin University
Changchun 130012, China
email: zhouqian@jlu.edu.cn

Return to the EJDE web page