Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion

Abstract

We considered a Cauchy problem of a one-dimensional semilinear wave equation with variable-coefficient diffusion, time-dependent damping, and perturbations. The global well-posedness and the asymptotic profile are given by employing scaling variables and the energy method. The lower bound estimate of the lifespan to the solution is obtained as a byproduct. For more information see https://ejde.math.txstate.edu/Volumes/2024/04/abstr.html