STRONG ASYMPTOTIC STABILITY FOR A BEAM EQUATION WITH WEAK DAMPING

Any solution to the problem u(tt) + d(x)beta(u(t)) + u(xxxx) = 0, x is-an-element-of (0, pi), t greater-than-or-equal-to 0, u = u(xx) = 0 for x = 0, pi, t greater-than-or-equal-to 0, u = u0, u(t) = u1 for t = 0, is shown to decay to zero in the strong topology of the energy space as t --> infinity. The function beta is allowed to be nonmonotone and d is a nonnegative function strictly positive on a nonvoid subset of (0, pi).