Weakly-damped focusing nonlinear Schrodinger equations with Dirichlet control

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Ozsari, Turker

关键词: Nonlinear Schrodinger equations;    Inhomogeneous Dirichlet boundary value;    Dynamic extension;    Hidden regularity;    Monotone operator theory;    Compactness method;    Global existence;    Exponential stabilization;   

DOI  :  10.1016/j.jmaa.2011.11.053

来源: Elsevier

【 摘 要 】

In this article we consider the weakly damped focusing nonlinear Schrodinger equations on bounded domains at the natural H-1-energy level with Dirichlet control acting on a portion of the boundary. We introduce the dynamic extension method for homogenizing the inhomogeneous boundary input. Then, we construct approximate solutions using monotone operator theory. A hidden trace regularity is proved to control the norm of the solutions in a global sense. This allows the use of compactness techniques by which we prove the existence of weak solutions. Finally, using multiplier techniques, we prove the exponential decay of solutions under the assumption that the boundary control also decays in a similar fashion. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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