Advertisement
Published in:
2009 | OriginalPaper | Chapter
Linear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control → Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay Rates
Authors : Irena Lasiecka, Roberto Triggiani
Published in: Sobolev Spaces in Mathematics III
Publisher: Springer New York
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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.