Browsing by Subject "noncylindrical domains"
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Item type:Article, Access status: Open Access , Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains(Wydawnictwa AGH, 2020) Nakao, MitsuhiroWe 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.