Iturriaga, Edgar and Leiva, Hugo (2010) A Characterization of Semilinear Surjective Operators and Applications to Control Problems. Applied Mathematics, 01 (04). pp. 265-273. ISSN 2152-7385
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Abstract
In this paper we characterize a broad class of semilinear surjective operators given by the following formula where Z are Hilbert spaces, and is a suitable nonlinear function. First, we give a necessary and sufficient condition for the linear operator to be surjective. Second, we prove the following statement: If and is a Lipschitz function with a Lipschitz constant small enough, then and for all the equation admits the following solution .We use these results to prove the exact controllability of the following semilinear evolution equation , , where , are Hilbert spaces, is the infinitesimal generator of strongly continuous semigroup in the control function belong to and is a suitable function. As a particular case we consider the semilinear damped wave equation, the model of vibrating plate equation, the integrodifferential wave equation with Delay, etc.
Item Type: | Article |
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Subjects: | Eprints STM archive > Mathematical Science |
Depositing User: | Unnamed user with email admin@eprints.stmarchive |
Date Deposited: | 03 Jun 2023 09:37 |
Last Modified: | 18 Nov 2023 05:38 |
URI: | http://public.paper4promo.com/id/eprint/562 |