Feedback stabilization of a marginally stable parabolic equation and a counterexample to a conjecture on this topic

Abstract

The first part of this paper is concerned with the exponential stabilization of certain marginally stable equations by means of a feedback. If you think of the standard Neumann problem for the Laplacian as an example of a marginally stable equation, there is the conjecture that for feedbacks with restricted sign the feedback system is always exponentially stable. We disprove this conjecture in the second part of our paper

Keywords:

• Marginal stability
• parabolic equations