Publication: Uniform decay rates for the energy of weakly damped defocusing semilinear Schrodinger equations with inhomogeneous Dirichlet boundary control
Program
KU-Authors
KU Authors
Co-Authors
Ozsari, Turker
Lasiecka, Irena
Advisor
Publication Date
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Abstract
In this paper, we study the open loop stabilization as well as the existence and regularity of solutions of the weakly damped defocusing semilinear Schrödinger equation with an inhomogeneous Dirichlet boundary control. First of all, we prove the global existence of weak solutions at the �1-energy level together with the stabilization in the same sense. It is then deduced that the decay rate of the boundary data controls the decay rate of the solutions up to an exponential rate. Secondly, we prove some regularity and stabilization results for the strong solutions in �2-sense. The proof uses the direct multiplier method combined with monotonicity and compactness techniques. The result for weak solutions is strong in the sense that it is independent of the dimension of the domain, the power of the nonlinearity, and the smallness of the initial data. However, the regularity and stabilization of strong solutions are obtained only in low dimensions with small initial and boundary data.
Description
Source:
Journal of Differential Equations
Publisher:
Elsevier
Keywords:
Subject
Mathematics