Carleman estimate for solutions to a degenerate convection-diffusion equation

Chunpeng Wang; Yanan Zhou; Runmei Du; Qiang Liu

doi:10.3934/dcdsb.2018133

Article Contents

2018, Volume 23, Issue 10: 4207-4222. Doi: 10.3934/dcdsb.2018133

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Carleman estimate for solutions to a degenerate convection-diffusion equation

1.
School of Mathematics, Jilin University, Changchun 130012, China
2.
School of Basic Science, Changchun University of Technology, Changchun 130012, China
3.
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

* Corresponding author: Qiang Liu
* Corresponding author: Qiang Liu

Received: August 31, 2017

Early access: April 2018

Published: September 2018

Supported by the National Natural Science Foundation of China (No. 11222106, 11571137 and 11401049), the Natural Science Foundation for Young Scientists of Jilin Province(20170520048JH), the Scientific and Technological project of Jilin Provinces Education Department in Thirteenth Five-Year(JJKH20170534KJ), NSF of Guangdong Province(2016A030313048) and Excellent Young Teachers Program of Guandon.

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Abstract

This paper concerns a control system governed by a convection-diffusion equation, which is weakly degenerate at the boundary. In the governing equation, the convection is independent of the degeneracy of the equation and cannot be controlled by the diffusion. The Carleman estimate is established by means of a suitable transformation, by which the diffusion and the convection are transformed into a complex union, and complicated and detailed computations. Then the observability inequality is proved and the control system is shown to be null controllable.

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Mathematics Subject Classification: 93B05, 93C20, 35K65.

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