General decay result for the wave equation with memory and acoustic boundary conditions. (January 2023)

• Record Type: Journal Article
• Authors: Yoon, Min; Lee, Mi Jin; Kang, Jum-Ran
• Is Part Of: Applied mathematics letters. Volume 135(2023)
• Publication Date: 2023-01
• Subjects: Optimal decay -- Viscoelastic wave equation -- Acoustic boundary conditions; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108385
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we are concerned with the energy decay rates for the viscoelastic wave equation with acoustic boundary conditions. Here we consider with minimal conditions on the L 1 ( 0, ∞ ) relaxation function α, namely α ′ ( t ) ≤ − ζ ( t ) G ( α ( t ) ), where G is an increasing and convex function near the origin and ζ is a nonincreasing function. Using the assumptions on the relaxation function α due to Mustafa (2018), we generalize the work of Park and Park (2011) and Liu (2014) to general decay.