Exponential decay estimates for semilinear wave-type equations with time-dependent time delay
Analysis of PDEs
2023-03-28 v1
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.
Cite
@article{arxiv.2303.14208,
title = {Exponential decay estimates for semilinear wave-type equations with time-dependent time delay},
author = {Cristina Pignotti},
journal= {arXiv preprint arXiv:2303.14208},
year = {2023}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2108.12786