Xiu-Fang Yu, Jun-Min Wang, Han-Wen Zhang
Abstract:
This article concerns the internal stabilization problem of 1-D interconnected heat-wave
equations, where information exchange and the two actuators occur at the adjacent
side of the two equations. By designing an inverse back-stepping transformation,
the original system is converted into a dissipative target system.
Moreover, we investigate the eigenvalues distribution and the corresponding
eigenfunctions of the closed-loop system by an asymptotic analysis method.
This shows that the spectrum of the system can be divided into two families:
one distributed along the a line parallel to the left side of the imaginary axis
and symmetric to the real axis, and the other on the left half real axis.
Then we work on the properties of the resolvent operator and we verify that
the root subspace is complete.
Finally, we prove that the closed-loop system is exponentially stable.
Submitted September 2, 2022. Published January 6, 2023.
Math Subject Classifications: 93C20, 93D15.
Key Words: Heat-wave equation; boundary control; spectrum; root subspace; exponential stability.
DOI: https://doi.org/10.58997/ejde.2023.03
Show me the PDF file (391 KB), TEX file for this article.
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Xiu-Fang Yu School of Mathematics and Statistics Beijing Institute of Technology Beijing 100081, China email: 15735185498@163.com |
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Jun-Min Wang School of Mathematics and Statistics Beijing Institute of Technology Beijing 100081, China email: jmwang@bit.edu.cn |
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Han-Wen Zhang School of Automation and Software Engineering Shanxi University Taiyuan Shanxi 030006, China email: zhanghanwen_mm@163.com |
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