Browsing by Subject "energy decay"

Now showing 1 - 2 of 2

Access status: Open Access ,
Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains
(Wydawnictwa AGH, 2020) Nakao, Mitsuhiro
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.
Access status: Open Access ,
Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity
(2014) Nakao, Mitsuhiro
We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a ‘loan’ method and use a difference inequality on the energy.