In this paper, we analyze a semilinear abstract damped wave-type equation with time delay. We assume that the delay feedback coefficient is variable in time and belongs to $L^1_{loc}([0,+\infty))$. Under suitable assumptions, we show well-posedness and exponential stability for small initial data. Our strategy combines careful energy estimates and continuity arguments. Some examples illustrate the abstract results.
Well-posedness and stability for semilinear wave-type equations with time delay
Cristina Pignotti
2022-01-01
Abstract
In this paper, we analyze a semilinear abstract damped wave-type equation with time delay. We assume that the delay feedback coefficient is variable in time and belongs to $L^1_{loc}([0,+\infty))$. Under suitable assumptions, we show well-posedness and exponential stability for small initial data. Our strategy combines careful energy estimates and continuity arguments. Some examples illustrate the abstract results.File in questo prodotto:
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