Controllability of partial differential equations on graphs

• Autorzy: Sergei Avdonin , Victor Mikhaylov
• Języki publikacji: EN

Abstrakty

EN

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 L₂-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.

Kategorie tematyczne

• 35P10: Completeness of eigenfunctions, eigenfunction expansions
• 94C15: Applications of graph theory
• 35K05: Heat equation
• 35L05: Wave equation
• 93B05: Controllability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2008
• Tom: 35
• Numer: 4
• Strony: 379-393

Daty

wydano

2008

Twórcy

autor

Sergei Avdonin

• Department of Mathematics and Statistics, University of Alaska, Fairbanks, AK 99775-6660, U.S.A.

autor

Victor Mikhaylov

• Department of Mathematics and Statistics, University of Alaska, Fairbanks, AK 99775-6660, U.S.A.

Identyfikatory

DOI

10.4064/am35-4-1