Bulletin of the Belgian Mathematical Society - Simon Stevin

On the Admissible Control operators for Linear and Bilinear Systems and the Favard Spaces

F. Maragh, H. Bounit, A. Fadili, and H. Hammouri

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Abstract

The objective of this work is to give some relationship between the Favard spaces and the $p$-admissibility (resp. $(p,q)$-admissibility) of unbounded control operators for linear (resp; bilinear) systems in Banach spaces. For linear case, this enables to give a simple identification of the space of the $1-$admissible control operators in Banach space and it enables us to extend the result of Weiss [29] (for $p=1$) on reflexive Banach spaces to a general situation. This result is applied to boundary control systems. The results obtained for bilinear systems generalize those given in Idrissi [16] and Berrahmoune [2] and are applied to diffusion equations of fractional order time distributed order.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 4 (2014), 711-732.

Dates
First available in Project Euclid: 23 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1414091010

Digital Object Identifier
doi:10.36045/bbms/1414091010

Mathematical Reviews number (MathSciNet)
MR3271328

Zentralblatt MATH identifier
1301.93046

Subjects
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25] 39A14: Partial difference equations 32A70: Functional analysis techniques [See mainly 46Exx] 93C25: Systems in abstract spaces 93C20: Systems governed by partial differential equations

Keywords
Infinite-dimensional systems semigroups Favard spaces unbounded linear (bilinear) control systems admissibility abstract linear (bilinear) control systems boundary control systems

Citation

Maragh, F.; Bounit, H.; Fadili, A.; Hammouri, H. On the Admissible Control operators for Linear and Bilinear Systems and the Favard Spaces. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 4, 711--732. doi:10.36045/bbms/1414091010. https://projecteuclid.org/euclid.bbms/1414091010


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