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Carleman estimate for parabolic equation with memory effects and exact controllability
Author(s) -
Kumarasamy Sakthivel
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700418
Subject(s) - controllability , observability , nonlinear system , mathematics , linearization , control theory (sociology) , point (geometry) , parabolic partial differential equation , mathematical analysis , control (management) , partial differential equation , computer science , physics , geometry , quantum mechanics , artificial intelligence
A nonlinear parabolic problem with memory effect is considered. We first establish a Carleman type estimate for a linear problem which is the adjoint of a suitable linearization of the nonlinear problem. As a consequence of this estimate we obtain an observability estimate. Then we establish the exact controllability of the linearized system with distributed control over a subdomain. Finally, we arrive at the controllability of the nonlinear system via a classical fixed point theorem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)