UPPER SEMICONTINUITY OF PULLBACK ATTRACTORS FOR NON-AUTONOMOUS KIRCHHOFF WAVE EQUATIONS

摘要

The paper investigates the upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations with structural damping: u(tt) - M(parallel to del u parallel to(2))Delta u+(-Delta)(alpha)u(t)+f(u) = g(x, t), where alpha is an element of (1/2, 1) is said to be a dissipative index. It shows that when the nonlinearity f(u) is of super-critical growth p : 1 = p p(alpha) equivalent to N+4 alpha/(N-4 alpha)(+), the related evolution process has a pullback attractor for each alpha is an element of (1/2, 1), and the family of pullback attractors is upper semicontinuous with respect to alpha. These results extend those in [27] for autonomous Kirchhoff wave models.