Well-posedness and stability for semilinear wave-type equations with time delay

Alessandro Paolucci; Cristina Pignotti

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arXiv · 2108.12786

Well-posedness and stability for semilinear wave-type equations with time delay

Alessandro Paolucci·Cristina Pignotti

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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 belonging 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.

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Alessandro Paolucci, Cristina Pignotti. 2021-08-29. Well-posedness and stability for semilinear wave-type equations with time delay. https://arxiv.org/abs/2108.12786

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