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

2021/08/29 by Alessandro Paolucci, Paolucci, Alessandro, Cristina Pignotti +1 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.12786

openalex publication_date 2021/08/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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 L¹_loc([0, +∞)). 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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• Indirect stabilization of nonlinear coupled wave equations in the presence of time delay or indefinite damping

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