STABILITY OF THE HEAT AND OF THE WAVE EQUATIONS WITH BOUNDARY TIME-VARYING DELAYS - Archive ouverte HAL
Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series S Année : 2009

STABILITY OF THE HEAT AND OF THE WAVE EQUATIONS WITH BOUNDARY TIME-VARYING DELAYS

Résumé

Exponential stability analysis via Lyapunov method is extended to the one-dimensional heat and wave equations with time-varying delay in the boundary conditions. The delay function is admitted to be time-varying with an a priori given upper bound on its derivative, which is less than 1. Sufficient and explicit conditions are derived that guarantee the exponential stability. Moreover the decay rate can be explicitly computed if the data are given.
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Dates et versions

hal-03579866 , version 1 (18-02-2022)

Identifiants

Citer

Serge Nicaise, Julie Valein, Emilia Fridman. STABILITY OF THE HEAT AND OF THE WAVE EQUATIONS WITH BOUNDARY TIME-VARYING DELAYS. Discrete and Continuous Dynamical Systems - Series S, 2009, 2 (3), pp.559-581. ⟨10.3934/dcdss.2009.2.559⟩. ⟨hal-03579866⟩
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