Contents Online
Methods and Applications of Analysis
Volume 29 (2022)
Number 3
A transmission problem for waves under time-varying delay and time-varying weights
Pages: 229 – 248
DOI: https://dx.doi.org/10.4310/MAA.2022.v29.n3.a1
Authors
Abstract
This manuscript focuses on in the transmission problem for one dimensional waves with time-varying 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.
Keywords
transmission problem, time-varying delay, time-varying weights, exponential stability
2010 Mathematics Subject Classification
35B40, 35L20, 93D15
Received 1 January 2021
Accepted 25 February 2022
Published 21 March 2023