@Article{Nakao2020,
author = "Nakao, Mitsuhiro",
title = "Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "6",
pages = "725--736",
doi = "https://doi.org/10.7494/OpMath.2020.40.6.725",
url = "https://doi.org/10.7494/OpMath.2020.40.6.725",
abstract = "We consider the initial-boundary value problem for semilinear dissipative wave equations in noncylindrical domain \(\bigcup_{0\leq t \lt\infty} \Omega(t)\times\{t\} \subset \mathbb{R}^N\times \mathbb{R}\). We are interested in finite energy solution. We derive an exponential decay of the energy in the case \(\Omega(t)\) is bounded in \(\mathbb{R}^N\) and the estimate \[\int\limits_0^{\infty} E(t)dt \leq C(E(0),\|u(0)\|)\lt \infty\] in the case \(\Omega(t)\) is unbounded. Existence and uniqueness of finite energy solution are also proved.",
keywords = "energy decay, global existence, semilinear wave equation, noncylindrical domains",
issn = "1232-9274"
}