TY - JOUR
T1 - Convergence Rate of Solutions to a Hyperbolic Equation with $p(x)$-Laplacian Operator and Non-Autonomous Damping
AU - Gao , Wenjie
AU - Li , Xiaolei
AU - Wang , Chunpeng
JO - Communications in Mathematical Research 
VL - 2
SP - 190
EP - 208
PY - 2023
DA - 2023/04
SN - 39
DO - http://doi.org/10.4208/cmr.2022-0060
UR - https://global-sci.org/intro/article_detail/cmr/21544.html
KW - Convergence rate, energy estimate, non-autonomous damping.
AB - <p style="text-align: justify;">This paper concerns the convergence rate of solutions to a hyperbolic
equation with $p(x)$-Laplacian operator and non-autonomous damping. We apply the Faedo-Galerkin method to establish the existence of global solutions,
and then use some ideas from the study of second order dynamical system to
get the strong convergence relationship between the global solutions and the
steady solution. Some differential inequality arguments and a new Lyapunov
functional are proved to show the explicit convergence rate of the trajectories.</p>