EXACT CONTROLLABILITY FOR PROBLEMS OF TRANSMISSION OF THE PLATE EQUATION WITH LOWER-ORDER TERMS

EXACT CONTROLLABILITY FOR PROBLEMS OF TRANSMISSION OF THE PLATE EQUATION WITH LOWER-ORDER TERMS

We consider the exact controllability for the problem of transmission of the plate equation with lower-order terms. Using Lions' Hilbert Uniqueness Method (HUM for short), we show that the system is exactly controllable in L²(Ω) × H⁻²(Ω). We also obtain some uniqueness theorems for the problem...

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Veröffentlicht in:Quarterly of applied mathematics 2000-03, Vol.58 (1), p.37-68
Hauptverfasser: LIU, WEIJIU, WILLIAMS, GRAHAM H.
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Boundary conditions
Boundary value problems
Eigenvalues
Mathematical analysis
Mathematical theorems
Uniqueness
Variational methods
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Zusammenfassung:We consider the exact controllability for the problem of transmission of the plate equation with lower-order terms. Using Lions' Hilbert Uniqueness Method (HUM for short), we show that the system is exactly controllable in L²(Ω) × H⁻²(Ω). We also obtain some uniqueness theorems for the problem of transmission of the plate equation and for the operator a(x)△² + q.
ISSN:0033-569X
1552-4485
DOI:10.1090/qam/1738557