Yuequn Li, Hui Liu, Fei Guo
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 8, 2024.
Math Subject Classifications: 35B44, 35G25.
Key Words: Semilinear damped wave equation; asymptotic profile; lifespan; scaling variables; energy method.
DOI: 10.58997/ejde.2023.04
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Yuequn Li School of Mathematical Sciences Nanjing Normal University Nanjing 210023, China email: liyuequn1997@163.com |
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Hui Liu School of Mathematical Sciences Nanjing Normal University Nanjing 210023, China email: 1412797891@qq.com |
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Fei Guo School of Mathematical Sciences and Key Laboratory for NSLSCS Ministry of Education, Nanjing Normal University Nanjing 210023, China email: guof@njnu.edu.cn |
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