Interior approximate controllability of second-order semilinear control systems
Anurag Shukla, N. Sukavanam
Abstract
In our manuscript, we investigate the interior approximate controllability for the subsequent semilinear second-order system in L2(Ω) s″(σ)+A0s(σ)=B0u(σ)+ξ(σ,s(σ)),0≤σ≤ϱs(0)=s0,s′(0)=s1, where A0 is the linear and unbounded operator, B0 is a bounded linear operator and ξ is a nonlinear operator defined on appropriate spaces. The proposed problem can be converted into an equivalent first-order semilinear control system, then the approximate controllability results for the proposed system are obtained from the study of the approximate controllability of the reduced first-order system. The Leray–Schauder alternative theorem and principle of contraction are used in the proof of our main theorems.
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