Global Attractor for Coupled Beam Equations with Nonhomogeneous Boundaries Conditions

摘要

We study the longtime behavior for thermoelastic coupled beam equations with strong damping and past history thermal memory U-tt + u(xxxx) + u(xxxxt) + theta(xx) - M(integral(1)(0)(u(x))(2)dx)u(xx) = h(x), in [0, l] x R+, and theta(t) - t theta(xx) - (1-t) integral(infinity)(0) k(s)theta(xx)(t - s)ds - u(xxt) + p(theta) = q(x) with 1/2 = t 1, where we consider the nonlinear boundary conditions u(0, t) = u(x)(0,t) = u(xx)(l,t) = 0, u(xxx)(l, t) + u(xxxt)(l, t) - M(integral(1)(0) u(x)(2)dx)u(x)(l, t) = f(u(l,t)) + g(u(t)(l, t)), theta(0, t) = theta(x)(l, 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 = 1.