Exponential time decay of solutions to a nonlinear fourth-order parabolic equation

In this paper we investigate the large-time behavior of weak solutions to the nonlinear fourth-order parabolic equation n(t) = -(n(log n)(xx))(xx) modeling interface fluctuations in spin systems. We study here the case x is an element of Omega = (0, 1), with n = 1, n(x) = 0 on partial derivativeOmega. In particular, we prove the exponential decay of u(x, t) towards the constant steady state n(infinity) = 1 in the L-1 norm for long times and we give the explicit rate of decay. The result is based on classical entropy estimates, and on detailed lower bounds for the entropy production.