Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 04, pp. 1-31.

Title: Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion
       
Authors: Yuequn Li (Nanjing Normal Univ., Nanjing, China)
         Hui Liu (Nanjing Normal Univ., Nanjing, China
         Fei Guo (Nanjing Normal Univ., Nanjing, China)

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.

Submitted August 27, 2023. Published January 08, 2024.
Math Subject Classifications: 35B44, 35G25.
Key Words: Semilinear damped wave equation; asymptotic profile; lifespan; scaling variables; 
  energy method.