Global Attractor for Coupled Beam Equations with Nonhomogeneous Boundaries Conditions

الملخص EN

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.