scholarly journals GLOBAL ATTRACTOR OF THE WEAKLY DAMPED WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS

2012 ◽  
Vol 27 (1) ◽  
pp. 97-106
Author(s):  
Chaosheng Zhu
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Global Attractor ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Damped Wave Equation

scholarly journals Global Attractor for Coupled Beam Equations with Nonhomogeneous Boundaries Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yuying Li ◽  
Haifeng Zhang
Keyword(s):  
Boundary Conditions ◽  
Global Attractor ◽  
Nonlinear Boundary ◽  
Initial Conditions ◽  
Past History ◽  
Nonlinear Boundary Conditions ◽  
Nonlinear Damping ◽  
Coupled Vibration ◽  
Beam Equations ◽  
Longtime Behavior

We study the longtime behavior for thermoelastic coupled beam equations with strong damping and past history thermal memory utt+uxxxx+uxxxxt+θxx-M∫0lux2dxuxx=hx, in 0,l×R+, and θt-ιθxx-1-ι∫0∞ksθxxt-sds-uxxt+pθ=qx, with 1/2≤ι<1, where we consider the nonlinear boundary conditions u0,t=ux0,t=uxxl,t=0, uxxxl,t+uxxxt(l,t)-M∫0lux2dxux(l,t)=ful,t+gutl,t,θ0,t=θxl,t=0 and certain initial conditions. To this problem little is known with nonlinear boundary conditions. This system arises from a model of the nonlinear thermoelastic coupled vibration beam with a nonlinear damping acting on x=l.

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