PORTUGALIAE MATHEMATICA Vol. 51, No. 2, pp. 243256 (1994) 

Stabilization of the Schrödinger EquationE. Machtyngier and E. ZuazuaInstituto de Matemática, U.F.R.J.,CP 68530, Rio de Janeiro, R.J. CEP 21944  BRASIL Departamento de Matemática Aplicada, Universidad Complutense, 28040 Madrid  SPAIN Abstract: We study the stabilization problem for Schrödinger equation in a bounded domain in two different situations. First, the boundary stabilization problem is considered. Dissipative boundary conditions are introduced. By using multiplier techniques and constructing energy functionals well adapted to the system, the exponential decay in $H^1$ is proved. On the other hand, the internal stabilization problem is considered. When the damping term is effective on a neighborhood of the boundary, the exponential decay in $L^2$ is proved by multiplier techniques. These results extend to Schrödinger equation recent results on the stabilizability of wave and plate equations. Keywords: Schrödinger equation; stabilization; dissipative boundary conditions; internal damping; multipliers; perturbed energy functionals. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1994 Sociedade Portuguesa de Matemática
