Analyticity and near optimal time boundary controllability for the linear Klein–Gordon equation

On the local energy decay of the synchronizable solutions of a coupled wave equations system

“…with p(t) → 0 when t → +∞. The energy decay property has important applications in many branches of theory of hyperbolic equations, in special in the in the aspects of the controllability theory for coupled wave systems (see previous works [1,2,[14][15][16]). Because of the importance of the energy decay subject, we have decided to study it in the aspect of the synchronization solution.…”

On the Exact Boundary Control for the Linear Klein-Gordon Equation in Non-cylindrical Domains

“…compactly supported in U, another essential element for the proof of the Theorem 1.1 is the analytic extension of the map t → (u(.,t), u t (.,t)) to the sector Σ 0 = {ζ = T 1 + z, |arg(z)| ≤ π/4} as proved in [17]. For our purpose, such result can be adapted in terms of the operators S t in the next lemma.…”

“…Then the family of compact linear operator {S t : t > d(U)} extends analytically to a family of linear compact operators {S ζ :, ζ ∈ Σ 0 }, where Σ 0 is complex sector {ζ = T 1 + z, |arg(z)| ≤ π 4 }, being T 1 any constant greater than d(Ω). The proof of the Lemma 2.2 is an immediate consequence of the Theorem 1.1 of[17] rewritten it in terms of operators S t .…”

Energy decay and control for a system of strings elastically connected in parallel

“…The analyticity of the solution operator , relative to the variable t as in Lemma , was first explored in the control for wave equation in Lagnese and for the Klein‐Gordon equation in Nunes and Bastos …”

“…In Rajaram and Najafi, the method HUM presented in Lions, was used to obtain the desirable control results. Here, as in Bastos et al and Nunes and Bastos, we use the controllability method presented by D.L. Russell .…”