Global existence and asymptotic profile for a damped wave equation with variable-coefficient diffusion
DOI:
https://doi.org/10.58997/ejde.2024.04Keywords:
Semilinear damped wave equation; asymptotic profile; lifespan; scaling variables; energy methodAbstract
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.
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Copyright (c) 2024 Yuequn Li, Hui Liu, Fei Guo
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