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Linear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control → Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay Rates

  • Irena Lasiecka
  • Roberto Triggiani
Part of the International Mathematical Series book series (IMAT, volume 10)

Abstrect

Abstract Uniform stabilization with nonlinear boundary feedback is asserted for classes of hyperbolic and Petrowski type multidimensional partial differential equations with variable coefficients (in space), as a consequence of the continuity (boundedness) of the corresponding purely Boundary Control → Boundary observation open-loop map of dissipative character, of interest in its own right. The interior is assumed inaccessible. There are explicit hyper-bolic/Petrowski type dynamical PDE classes where such a property holds and classes where it fails. When available, it has a number of attractive and unexpected consequences. In particular, when accompanied by exact controllability of the corresponding open-loop linear model, it implies uniform stabilization with optimal decay rates—when a nonlinear function of the boundary observation closes up the loop, to generate the corresponding boundary feedback dissipative problem.

Keywords

Boundary Control Lower Order Term Exact Controllability Contraction Semigroup Optimal Regularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. 1.University of VirginiaCharlottesvilleUSA

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