Feedback Stabilizability of Time-Periodic Parabolic Equations

  • Pablo Koch Medina
Part of the Dynamics Reported book series (DYNAMICS, volume 5)


Differential equations (partial and ordinary) have traditionally occupied a prominent place within mathematics. One of the main reasons for this is the fact that they have served as models for the evolution of systems arising in physics, chemistry, biology and various other disciplines. However, the traditional topics in the theory of differential equations do not encompass many important problems which fall into the realm of what is today known as control theory. In this paper we describe the basis for a geometric theory of time-periodic abstract linear control systems of ‘parabolic’ type, concentrating on stabilization by feedback, and discuss some applications to second order time-periodic parabolic initial-boundary value problems on bounded domains. A theory of this kind has already been developed in the finite dimensional case (cf. [17], [16]) and in infinite dimensions when the system is autonomous (cf. [7], [40]). For the time-periodic infinite dimensional case some first steps have been made by A. Lunardi (cf. [33]). But before we embark on a description of our results we give an example as motivation for the kind of problems in control theory we shall be concerned with.


Banach Space Exponential Stability Evolution Operator Mild Solution Zero Solution 
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Copyright information

© Springer-Verlar Berlin Heidelberg 1996

Authors and Affiliations

  • Pablo Koch Medina
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichSwitzerland

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