# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Uniform boundary controllability of a discrete 1-D wave equation. (English) Zbl 1157.93324
Summary: A numerical scheme for the controlled discrete 1-D wave equation is considered. We prove the convergence of the boundary controls of the discrete equations to a control of the continuous wave equation when the mesh size tends to zero when time and space steps coincide. This positive result is in contrast with previous negative ones for space semi-discretizations.

##### MSC:
 93B05 Controllability 93C20 Control systems governed by PDE
Full Text:
##### References:
 [1] J.A. Infante, E. Zuazua, Boundary observability for the space discretization of the one-dimensional wave equation, C.R. Acad. Sci. Paris, Ser. I Math. 326 (6) (1998) 713--718. · Zbl 0910.65051 [2] Isaacson, E.; Keller, H. B.: Analysis of numerical methods. (1966) · Zbl 0168.13101 [3] J.L. Lions, Contrôlabilité Exacte Perturbations et Stabilisation de Systèmes Distribués, Vols. 1 and 2, Masson, Paris, 1988. [4] S. Micu, Uniform boundary controllability of a semi-discrete 1-D wave equation, Numer. Math. 91 (4) (2002) 723--768. · Zbl 1002.65072 [5] Strauss, W.; Vazquez, L.: Numerical solution of a nonlinear Klein-Gordon equation. J. comput. Phys. 28, No. 2, 271-278 (1978) · Zbl 0387.65076