Uniform exponential stabilization and the state reconstruction of the wave equation with viscosity

Zheng, Fu; Yibo, Guan; Liu, Jiankang; Guo, Bao‐Zhu

doi:10.1360/ssm-2020-0292

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2023

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Cited by 2 publications

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“…For a regular enough solution z = z(t, x) of (1.1), we define its energy by Fu and Xu [8] Previous works [9,10]…”

Section: Introductionmentioning

confidence: 99%

Stabilization of the heat equation with disturbance at the flux boundary condition

Guzmán

Hernández

2023

Math Methods in App Sciences

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In this paper, we address the problem of boundary stabilization of the heat equation subjected to an unknown disturbance, which is assumed to be acting at the flux boundary condition. By means of Lyapunov techniques and the use of the sign multivalued operator, which is responsible of rejecting the effects of the disturbance, we design a multivalued feedback law to obtain the exponential stability of the closed‐loop system. The well‐posedness of the closed‐loop system, which is a differential inclusion, is shown with the maximal monotone operator theory.

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“…For a regular enough solution z = z(t, x) of (1.1), we define its energy by Fu and Xu [8] Previous works [9,10]…”

Section: Introductionmentioning

confidence: 99%

Stabilization of the heat equation with disturbance at the flux boundary condition

Guzmán

Hernández

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

The exponential stabilization of a heat-wave coupled system and its approximation

Zheng

Si-jia

Wang

et al. 2023

Journal of Mathematical Analysis and Applications

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Uniform exponential stabilization and the state reconstruction of the wave equation with viscosity

Cited by 2 publications

References 57 publications

Stabilization of the heat equation with disturbance at the flux boundary condition

Stabilization of the heat equation with disturbance at the flux boundary condition

The exponential stabilization of a heat-wave coupled system and its approximation

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