English

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.

Keywords

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

R2 v1 2026-06-28T09:32:46.676Z