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arXiv · 2609.08986

Well-posedness and exponential stability for abstract evolution equations with delay in the nonlinear source: frictional and viscoelastic cases

Houria Chellaoua·Yamna Boukhatem·Cristina Pignotti
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Abstract

In this paper, we establish the well-posedness and exponential stability of a class of semilinear neutral abstract evolution equations with constant time delay. Two damping mechanisms are considered: frictional damping of the form $CC^*u_t$ and viscoelastic damping with memory. Under suitable assumptions, we prove global well-posedness and exponential decay of solutions for sufficiently small initial data. This result is of considerable importance, as it provides a unified framework for the analysis of a wide class of neutral systems arising in structural mechanics, seismic isolation, and control theory. The abstract results are illustrated by some concrete examples. The analysis relies on a combination of semigroup theory, energy estimates, Duhamel's formula, and Gronwall-type arguments.

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Houria Chellaoua, Yamna Boukhatem, Cristina Pignotti. 2026-09-08. Well-posedness and exponential stability for abstract evolution equations with delay in the nonlinear source: frictional and viscoelastic cases. https://arxiv.org/abs/2609.08986

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