Internal stabilization of interconnected heat-wave equations
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Date
2023-01-06
Authors
Yu, Xiu-Fang
Wang, Jun-Min
Zhang, Han-Wen
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Heat-wave equation, Boundary control, Spectrum, Root subspace, Exponential stability
Citation
Yu, X. F., Wang, J. M., & Zhang, H. W. (2023). Internal stabilization of interconnected heat-wave equations. Electronic Journal of Differential Equations, 2023(03), pp. 1-26.
Rights
Attribution 4.0 International