Electron. J. Differential Equations, Vol. 2025 (2025), No. 04, pp. 1-17.

Exact controllability for degenerate and singular wave equations

Guang Zhang, Shugen Chai

Abstract:
In this article, we study exact controllability for degenerate and singular wave equations with a general coefficient. We estimate the observability inequality by the multiplier method and determine the observability time. We also deduce the exact controllability of the corresponding degenerate and singular control problem at a sufficiently large time, employing the Hilbert uniqueness method.

Submitted September 18, 2024. Published January 9, 2025.
Math Subject Classifications: 35L80, 35L81, 35L05, 93B05.
Key Words: Degenerate wave equation; singular wave equation; controllability; boundary control.
DOI: 10.58997/ejde.2025.04

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Guang Zhang
School of Mathematics and Statistics
Shanxi University
Taiyuan 030006, China
email: gzhang1231@163.com
Shugen Chai
School of Mathematics and Statistics
Shanxi University
Taiyuan 030006, China
email: sgchai@sxu.edu.cn

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