Paper Info
Title
Stabilisation Of Schrodinger Equation In Dynamic Boundary Feedback With A Memory-Typed Heat Equation
Abstract
In this work, we study the dynamic behaviour for a heat equation with exponential polynomial kernel memory to be a controller for a Schrodinger system. By introducing some new variables, the time-variant system is transformed into a time-invariant one. Remarkably, the resolvent of the closed-loop system operator is not compact anymore. The residual spectrum is shown to be empty and the continuous spectrum consisting of finite isolated points are obtained. It is shown that the sequence of generalised eigenfunctions forms a Riesz basis for the Hilbert state space. This deduces the spectrum-determined growth condition for the C-0-semigroup, and the exponential stability is then established.
Year
DOI
Venue
2019
10.1080/00207179.2017.1358826
INTERNATIONAL JOURNAL OF CONTROL
Keywords
DocType
Volume
Schrodinger equation, heat equation with memory, spectrum, asymptotic analysis, Riesz basis, exponential stability
Journal
92
Issue
ISSN
Citations 
2
0020-7179
0
PageRank 
References 
Authors
0.34
3
2
Name
Order
Citations
PageRank
Lu Lu100.34
Jun-Min Wang221929.95