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The Necessary and Sufficient Conditions of Exponential Stability for Heat and Wave Equations with Memory

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Abstract

This paper is addressed to a study of the stability of heat and wave equations with memory The necessary and sufficient conditions of the exponential stability are investigated by the theory of Laplace transform. The results show that the stability depends on the decay rate and the coefficient of the kernel functions of the memory. Besides, the feedback stabilization of the heat equation is obtained by constructing finite dimensional controller according to unstable eigenvalues. This stabilizing procedure is easy to operate and can be applicable for other parabolic equations with memory.

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Correspondence to Xiuxiang Zhou.

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The authors declare no conflict of interest.

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This research was supported by the National Science Foundation of China under Grant Nos. 12001087, 12001094 and 11871142.

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Li, L., Zhang, X. & Zhou, X. The Necessary and Sufficient Conditions of Exponential Stability for Heat and Wave Equations with Memory. J Syst Sci Complex 37, 1037–1051 (2024). https://doi.org/10.1007/s11424-023-2312-8

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  • DOI: https://doi.org/10.1007/s11424-023-2312-8

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