General decay result for the wave equation with memory and acoustic boundary conditions. (January 2023) - Yoon, Min; Lee, Mi Jin; Kang, Jum-Ran
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.