Uniform stabilization of the fourth order Schrodinger equation

We study both boundary and internal stabilization problems for the fourth order Schrodinger equation in a smooth bounded domain Omega of R-n. We first consider the boundary stabilization problem. By introducing suitable dissipative boundary conditions, we prove that the solution decays exponentially in an appropriate energy space. In the internal stabilization problem, by assuming that the damping term is effective on a neighborhood of a part of the boundary, we prove the exponential decay of the L-2(Omega)-energy of the solution. Both results are established by using multiplier techniques and compactness/uniqueness arguments. (C) 2016 Elsevier Inc. All rights reserved.