Existence, uniqueness and uniform decay for the nonlinear beam degenerate equation with weak damping

Global solution and asymptotic behavior for the variable coefficient beam equation with nonlinear damping

“…After that, there is a large literature focused on the existence, stability, and decay properties of global solutions for the n dimensional beam equation. We refer to [11][12][13][14] for linear damping case and to [15][16][17][18] for nonlinear damping case.…”

General Decay for the Degenerate Equation with a Memory Condition at the Boundary

“…The existence of global solutions and exponential decay to the degenerate equation with Ω = Γ 0 has been investigated by several authors. See Cavalcanti et al [1] and Menezes et al [2]. For instance, when ( ) is equal to 1, (1) describes the transverse deflection ( , ) of beams.…”