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Stability of the heat and of the wave equations with boundary time-varying delays

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  • 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.
    Mathematics Subject Classification: Primary: 93D15; Secondary: 35L05.

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