Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I

In this paper, we are interested in the Cauchy problem for viscoelastic damped wave equation with memory of type I. By applying WKB analysis and Fourier analysis, explain memory’s influence on dissipative structures asymptotic profiles solutions to model additionally weighted L 1 initial data. Furthermore, concerning standard energy solution itself, establish singular limit between Moore–Gibson–Thompson memory, where a crucial compatibility condition datum is found.