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Approximate Controllability of a Class of Semilinear Coupled Degenerate Systems

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Abstract

In this paper, we study the approximate controllability of a class of semilinear systems governed by coupled degenerate parabolic equations. The equations may be weakly degenerate and strongly degenerate on a portion of the lateral boundary. We prove that the control systems are approximately controllable by using the Kakutani fixed point theorem and the controls can be taken to be of quasi bang-bang form.

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Acknowledgments

The authors would like to express their sincerely thanks to the referees and the editor for their helpful comments on the original version of the paper.

Funding

This study was financially supported by the National Natural Science Foundation of China (Nos. 11925105 and 11801211).

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Correspondence to Qian Zhou.

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Xu, F., Zhou, Q. & Nie, Y. Approximate Controllability of a Class of Semilinear Coupled Degenerate Systems. J Dyn Control Syst 27, 31–49 (2021). https://doi.org/10.1007/s10883-020-09484-4

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  • DOI: https://doi.org/10.1007/s10883-020-09484-4

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