TY  - JOUR
ID  - Nakao2020
LB  - Nakao2020
AU  - Nakao, Mitsuhiro
TI  - Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains
ST  - Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 6
SP  - 725
EP  - 736
DO  - https://doi.org/10.7494/OpMath.2020.40.6.725
UR  - https://doi.org/10.7494/OpMath.2020.40.6.725
AB  - 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.
KW  - energy decay
KW  - global existence
KW  - semilinear wave equation
KW  - noncylindrical domains
SN  - 1232-9274
ER  -