Geodesic
Controllability of partial differential equations on graphs
Sergei Avdonin1 ; Victor Mikhaylov1
1 Department of Mathematics and Statistics University of Alaska Fairbanks, AK 99775-6660, U.S.A.
Applicationes Mathematicae, Tome 35 (2008) no. 4, pp. 379-393 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting through the Dirichlet condition applied to all or all but one boundary vertices. Exact controllability in $L_2$-classes of controls is proved and sharp estimates of the time of controllability are obtained for the wave equation. Null controllability for the heat equation and exact controllability for the Schrödinger equation in any time interval are obtained.
DOI : 10.4064/am35-4-1
Keywords: study boundary control problems wave heat schr dinger equations finite graph suppose graph tree does contain cycles each edge equation defined control acting through dirichlet condition applied all boundary vertices exact controllability classes controls proved sharp estimates time controllability obtained wave equation null controllability heat equation exact controllability schr dinger equation time interval obtained

Sergei Avdonin 1 ; Victor Mikhaylov 1

1 Department of Mathematics and Statistics University of Alaska Fairbanks, AK 99775-6660, U.S.A. 
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Sergei Avdonin; Victor Mikhaylov. Controllability of partial differential
 equations on graphs. Applicationes Mathematicae, Tome 35 (2008) no. 4, pp. 379-393. doi: 10.4064/am35-4-1

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