Advances in Differential Equations

Exact internal controllability for the magnetohydrodynamic equations in multi-connected domains

Teodor Havârneanu, Cătălin Popa, and S. S. Sritharan

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Abstract

We study the exact controllability for the magnetohydrodynamic equations in multi-connected bounded domains. We show that the value of any solution of the magnetohydrodynamic system at any given time is locally exactly controllable provided that this solution is smooth enough. This means that the chosen value of such a solution can be reached by starting from initial states which are sufficiently close to the initial value of the solution and by acting with controls distributed in a given small subdomain. So, a previous controllability result for the magnetohydrodynamic equations is improved in several directions. Our treatment reduces the local controllability for the magnetohydrodynamic equations to the global controllability for their linearizations by means of an infinite-dimensional variant of the local inversion theorem. The proof of the global controllability relies on a Carleman-type estimate for the adjoint linearized equations.

Article information

Source
Adv. Differential Equations Volume 11, Number 8 (2006), 893-929.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867619

Mathematical Reviews number (MathSciNet)
MR2261734

Zentralblatt MATH identifier
1167.35434

Subjects
Primary: 93B05: Controllability
Secondary: 35Q35: PDEs in connection with fluid mechanics 35Q60: PDEs in connection with optics and electromagnetic theory 76D55: Flow control and optimization [See also 49Q10, 93C20, 93C95] 76W05: Magnetohydrodynamics and electrohydrodynamics 93B07: Observability

Citation

Havârneanu, Teodor; Popa, Cătălin; Sritharan, S. S. Exact internal controllability for the magnetohydrodynamic equations in multi-connected domains. Adv. Differential Equations 11 (2006), no. 8, 893--929. https://projecteuclid.org/euclid.ade/1355867619.


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