Electron. J. Differential Equations, Vol. 2018 (2018), No. 195, pp. 1-20.

Carleman estimate and null controllability of a cascade degenerate parabolic system with general convection terms

Jianing Xu, Chunpeng Wang, Yuanyuan Nie

Abstract:
This article shows Carleman estimate and null controllability of a cascade control system governed by the semilinear degenerate parabolic equations with the general convection terms. The semilinear parabolic equations are weakly degenerate on the boundary and the convection terms cannot be controlled by the diffusion terms. We establish the Carleman estimate and the observability inequality for the linear conjugate system, and prove that the control system is null controllable.

Submitted April 2, 2018. Published December 6, 2018.
Math Subject Classifications: 93B05, 93C20, 35K67.
Key Words: Carleman estimate; null controllability; convection; degenerate parabolic system.

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Jianing Xu
School of Mathematics
Jilin University
Changchun 130012, China
email: 924751144@qq.com
Chunpeng Wang
School of Mathematics
Jilin University
Changchun 130012, China
email: wangcp@jlu.edu.cn
Yuanyuan Nie
School of Mathematics
Jilin University
Changchun 130012, China
email: nieyy@jlu.edu.cn

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