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

Carlos A. S. Nonato (Department of Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil)

Carlos A. Raposo (Department of Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil)

Waldemar D. Bastos (Department of Mathematics, São Paulo State University, São José do Rio Preto, São Paulo, Brazil)

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

Full Text (PDF format)

Received 1 January 2021

Accepted 25 February 2022

Published 21 March 2023