MADHUMITA ROY, Doctoral Student
Authors: Irena Lasiecka, Jose Rodrigues
2023 AWM Research Symposium
Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]
The purpose of this paper is to address long-term behavior of solutions to a plate model describing a suspension bridge with mixed boundary condition in presence of wind-effect and polynomial type weak damping. We prove the wellposed of the dynamical system by the traditional theory of nonlinear semigroups and monotone operators. Existence of the global attractor is shown by constructing an Absorbing set and then showing quasi-stability property of the system. Due to the presence of the term $u_y$, the dynamical system becomes non-Gradient; to overcome this crisis we use the textit{Barrier's} method for the construction of the Absorbing set.