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- Publisher
- Oxford University Press
- Copyright
- © Institute of Mathematics and its Applications 2005; all rights reserved. For permissions please email: journals.permissions@oupjournals.org
- ISSN
- 0265-0754
- eISSN
- 1471-6887
- DOI
- 10.1093/imamci/dni023
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we give a necessary and sufficient algebraic condition for the approximate controllability of the following system of parabolic equations with Dirichlet boundary condition:{zt = D Δz + b1(x)u1 + ··· + bm(x)um, t ≥ 0, z ∈ ℝn,z = 0, on ∂Ωwhere Ω is a sufficiently smooth bounded domain in ℝN, bi ∈ L2(Ω; ℝn), the control functions ui ∈ L2(0, t1; ℝ); i = 1, 2, …, m and D is an n × n non-diagonal matrix whose eigenvalues are semi-simple with positive real part. This algebraic condition is checkable since it is given in terms of the nγj × m matrices DPj and PjB, i.e.Rank [PjB⋮DPjB⋮D2PjB⋮··· Dnγj−1 PjB] = nγj,where PjBu = Pjb1u1 + ··· + Pjbmum. Finally, this result can be applied to those systems of partial differential equations that can be rewritten as a diffusion system (see de Oliveira, 1998).
Journal
IMA Journal of Mathematical Control and Information – Oxford University Press
Published: Jun 1, 2005