Israel Journal of Mathematics

, Volume 125, Issue 1, pp 83–92 | Cite as

Exact controllability for the wave equation with variable coefficients

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Abstract

We consider in this paper the evolution systemy″−Ay=0, whereA =∂ i(aij∂j) anda ij ∈C 1 (ℝ+;W 1,∞ (Ω)) ∩W 1,∞ (Ω × ℝ+), with initial data given by (y 0,y 1) ∈L 2(Ω) ×H −1 (Ω) and the nonhomogeneous conditiony=v on Γ ×]0,T[. Exact controllability means that there exist a timeT>0 and a controlv such thaty(T, v)=y′(T, v)=0. The main result of this paper is to prove that the above system is exactly controllable whenT is “sufficiently large”. Moreover, we obtain sharper estimates onT.

Keywords

Weak Solution Dirichlet Boundary Condition Strong Solution Hyperbolic System Sharp Estimate 
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Copyright information

© Hebrew University 2001

Authors and Affiliations

  1. 1.Institut de recherche mathématique avancéeUniversité Louis Pasteur et CNRSStrasbourg CédexFrance

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