scholarly journals Global attractor for a suspension bridge problem with a nonlinear delay term in the internal feedback

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Wenjun Liu ◽  
◽  
Hefeng Zhuang
Keyword(s):  
Global Attractor ◽  
Suspension Bridge ◽  
Internal Feedback ◽  
Delay Term ◽  
Bridge Problem ◽  
Nonlinear Delay

scholarly journals Finite dimensional global attractor for a suspension bridge problem with delay

2016 ◽  
Vol 354 (8) ◽  
pp. 808-824 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Soh E. Mukiawa ◽  
Enyi D. Cyril
Keyword(s):  
Global Attractor ◽  
Suspension Bridge ◽  
Finite Dimensional ◽  
Bridge Problem

Stabilization of the wave equation with a nonlinear delay term in the boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wassila Ghecham ◽  
Salah-Eddine Rebiai ◽  
Fatima Zohra Sidiali
Keyword(s):  
Wave Equation ◽  
Original Problem ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Decay Rates ◽  
Uniform Decay ◽  
Delay Term ◽  
Nonlinear Semigroup Theory ◽  
Nonlinear Boundary Feedback ◽  
Nonlinear Delay

Abstract A wave equation in a bounded and smooth domain of ℝ n {\mathbb{R}^{n}} with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.

scholarly journals Stability result of a suspension bridge Problem with time-varying delay and time-varying weight

2021 ◽  
Author(s):  
Soh Edwin Mukiawa
Keyword(s):  
Stability Result ◽  
Suspension Bridge ◽  
Energy Functional ◽  
Weight Functions ◽  
Time Varying ◽  
Plate Equation ◽  
Time Varying Delay ◽  
Bridge Problem ◽  
Plate Equations ◽  
Varying Delay

AbstractIn this paper, we study a plate equation as a model for a suspension bridge with time-varying delay and time-varying weights. Under some conditions on the delay and weight functions, we establish a stability result for the associated energy functional. The present work extends and generalizes some similar results in the case of wave or plate equations.

scholarly journals Long-Term Damped Dynamics of the Extensible Suspension Bridge

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Ivana Bochicchio ◽  
Claudio Giorgi ◽  
Elena Vuk
Keyword(s):  
Nonlinear Equation ◽  
Global Attractor ◽  
Axial Load ◽  
Suspension Bridge ◽  
External Source ◽  
Optimal Regularity ◽  
Absorbing Sets ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Equation

This work is focused on the doubly nonlinear equation , whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness . When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load and stiffness . For a general external source , we prove the existence of bounded absorbing sets. When is time-independent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.

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