Exponential stability of abstract evolution equations with time delay

2014/05/08 by Serge Nicaise, Nicaise, Serge, Cristina Pignotti +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1405.1850

openalex publication_date 2014/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the C₀-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a suitable smallness condition on the time delay feedback is satisfied. Some examples illustrating our abstract approach are also given.

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• Evolutionary equations with state-dependent delay

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