TY - JOUR
T1 - Existence of Global Attractor for Weakly Damped FDS Nonlinear Wave Equations
AU - Guo , Boling
AU - Zhang , Ying
JO - Annals of Applied Mathematics
VL - 4
SP - 333
EP - 346
PY - 2025
DA - 2025/01
SN - 40
DO - http://doi.org/10.4208/aam.OA-2024-0009
UR - https://global-sci.org/intro/article_detail/aam/23775.html
KW - Global attractors, a priori estimate, FDS nonlinear wave equations.
AB - <p style="text-align: justify;">The paper investigates the well-posedness of global solutions and the
existence of global attractors for weakly damped FDS nonlinear wave equations.
It establishes the well-posedness of weak solutions using Galerkin approximation
and a priori estimate. Subsequently, a dynamical system is constructed based
on the well-posedness of the solution. The existence of a bounded absorbing
set for the equations and the smooth properties of the operator semigroup are
presented, leading to the existence of a global attractor.</p>