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Journal Articles SIAM Journal on Control and Optimization Year : 2002

Indirect Boundary Stabilization of Weakly Coupled Hyperbolic Systems

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Abstract

This work is concerned with the boundary stabilization of an abstract system of two coupled second order evolution equations wherein only one of the equations is stabilized (indirect damping; see, e.g., J. Math. Anal. Appl., 173 (1993), pp. 339--358). We show that, under a condition on the operators of each equation and on the boundary feedback operator, the energy of smooth solutions of this system decays polynomially at ∞. We then apply this abstract result to several systems of partial differential equations (wave-wave systems, Kirchhoff--Petrowsky systems, and wave-Petrowsky systems)
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Dates and versions

hal-03895241 , version 1 (12-12-2022)

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Fatiha Alabau-Boussouira. Indirect Boundary Stabilization of Weakly Coupled Hyperbolic Systems. SIAM Journal on Control and Optimization, 2002, 41 (2), pp.511-541. ⟨10.1137/S0363012901385368⟩. ⟨hal-03895241⟩
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