Exponential decay estimates for semilinear wave-type equations with time-dependent time delay

2023/03/24 by Pignotti, Cristina · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.14208

Abstract

In this paper, we analyze a semilinear damped second order evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. The nonlinear term satisfies a local Lipschitz continuity assumption. Under appropriate conditions, we prove well-posedness and exponential stability of our model for small initial data. Our arguments combine a Lyapunov functional approach with some continuity arguments. Moreover, as an application of our abstract results, the damped wave equation with a source term and delay feedback is analyzed.

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• Indirect stabilization of nonlinear coupled wave equations in the presence of time delay or indefinite damping

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