Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    On boundary controllability of a vibrating plate (1985)
    Springer
    Applied mathematics & optimization 13 (1985), S. 205-229 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A vibrating plate is here taken to satisfy the model equation:u tt + Δ2u = 0 (whereΔ 2u:= Δ(Δu); Δ = Laplacian) with boundary conditions of the form:u v = 0 and(Δu) v = ϕ = control. Thus, the state is the pair [u, u t] and controllability means existence ofϕ on Σ:= (0,T)×∂Ω transfering ‘any’[u, u t]0 to ‘any’[u, u t]T. The formulation is given by eigenfunction expansion and duality. The substantive results apply to a rectangular plate. For largeT one has such controllability with∥ϕ∥ = O(T −1/2). More surprising is that (based on a harmonic analysis estimate [11]) one has controllability for arbitrarily short times (in contrast to the wave equation:u tt = Δu) with log∥ϕ∥ = O(T −1) asT→0. Some related results on minimum time control are also included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442208
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Exact boundary controllability of an integrodifferential equation (1987)
    Springer
    Applied mathematics & optimization 15 (1987), S. 223-250 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An integrodifferential equation of the Volterra type is considered under the action of anL 2(0, T, L2(Γ))-boundary control. By harmonic analysis arguments it is shown that the controllability results obtained in [17] for the underlying reference model associated with a trivial convolution kernel, carry over to the model under consideration without any smallness assumption concerning the memory kernel.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442653
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Domain Decomposition of Optimal Control Problems for Dynamic Networks of Elastic Strings (2000)
    Springer
    Computational optimization and applications 16 (2000), S. 5-27 
    Details
    ISSN: 1573-2894
    Keywords: dynamic networks of elastic strings ; dynamic domain decomposition ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider optimal control problems related to exact- and approximate controllability of dynamic networks of elastic strings. In this note we concentrate on problems with linear dynamics, no state and no control constraints. The emphasis is on approximating target states and velocities in part of the network using a dynamic domain decomposition method (d3m) for the optimality system on the network. The decomposition is established via a Uzawa-type saddle-point iteration associated with an augmented Lagrangian relaxation of the transmission conditions at multiple joints. We consider various cost functions and prove convergence of the infinite dimensional scheme for an exemplaric choice of the cost. We also give numerical evidence in the case of simple exemplaric networks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008721402512
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Boundary control of a vibrating plate with internal damping (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 573-586 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that finite energy states of a vibrating viscoelastic plate of the Kelvin-Voigt type are, in general, not exactly controllable by L2-boundary controls. Accordingly, we present a result on approximative controllability. The method is general.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110502
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Book
    Book
    Domain decomposition methods in optimal control of partial differential equations /; 148 (2004)
    Basel [u.a.] :Birkhäuser,
    Details
    Title: Domain decomposition methods in optimal control of partial differential equations /; 148
    Author: Lagnese, John E.
    Contributer: Leugering, Günter
    Publisher: Basel [u.a.] :Birkhäuser,
    Year of publication: 2004
    Pages: XIII, 443 S. : , Ill.
    Series Statement: International series of numerical mathematics 148
    ISBN: 3-7643-2194-6
    Type of Medium: Book
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    ZIB Catalog
    Zuse Institute Berlin get availability status
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...