A transmission problem for waves under time-varying delay and nonlinear weight

TL;DR

This paper investigates a one-dimensional wave transmission problem with nonlinear damping and time-varying delay, establishing global existence and exponential stability through energy methods and Lyapunov functionals.

Contribution

It introduces a novel analysis of wave transmission with nonlinear weights and delays, proving global solutions and stability.

Findings

Global existence of solutions proven

Exponential stability established

Effective Lyapunov functional constructed

Abstract

This manuscript focus on in the transmission problem for one dimensional waves with nonlinear weights on the frictional damping and time-varying delay. We prove global existence of solutions using Kato's variable norm technique and we show the exponential stability by the energy method with the construction of a suitable Lyapunov functional.