Interior Controllability of a Broad Class of Reaction Diffusion Equations
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-07-14
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We prove the interior approximate controllability of the following broad class of reaction diffusion equation in the Hilbert spaces Z=L2(Ω) given by z′=−Az+1ωu(t), t∈[0,τ], where Ω is a domain in ℝn, ω is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u∈L2(0,t1;L2(Ω)) and A:D(A)⊂Z→Z is an unbounded linear operator with the following spectral decomposition: Az=∑j=1∞λj∑k=1γj〈z,ϕj,k〉ϕj,k.
The eigenvalues 0<λ1<λ2<⋯<⋯λn→∞ of A have finite multiplicity γj equal to the dimension of the corresponding eigenspace, and {ϕj,k} is a complete orthonormal set of eigenvectors of A.
The operator −A generates a strongly continuous semigroup {T(t)} given by T(t)z=∑j=1∞e−λjt∑k=1γj〈z,ϕj,k〉ϕj,k.
Our result can be applied to the nD heat equation, the Ornstein-Uhlenbeck equation, the Laguerre equation, and the Jacobi equation.
American Psychological Association (APA)
Leiva, Hugo& Quintana, Yamilet. 2009. Interior Controllability of a Broad Class of Reaction Diffusion Equations. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-8.
https://search.emarefa.net/detail/BIM-492270
Modern Language Association (MLA)
Leiva, Hugo& Quintana, Yamilet. Interior Controllability of a Broad Class of Reaction Diffusion Equations. Mathematical Problems in Engineering No. 2009 (2009), pp.1-8.
https://search.emarefa.net/detail/BIM-492270
American Medical Association (AMA)
Leiva, Hugo& Quintana, Yamilet. Interior Controllability of a Broad Class of Reaction Diffusion Equations. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-8.
https://search.emarefa.net/detail/BIM-492270
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-492270