Approximate controllability of semilinear impulsive evolution equations

Abstract:

We prove the approximate controllability of the following semilinear impulsive evolution equation: z'=Az+Bu(t)+F(t,z,u), z∈Z, t∈(0,τ], z(0)=z0, z(tk+)=z(tk-)+Ik(tk,z(tk),u(tk)), k=1,2,3,.,p, where 0<t1<t2<t3<<tp<τ, Z and U are Hilbert spaces, u∈L2(0,τ;U), B:U→Z is a bounded linear operator, Ik,F:[0,τ]×Z×U→Z are smooth functions, and A:D(A)⊂Z→Z is an unbounded linear operator in Z which generates a strongly continuous semigroup {T(t)}t≥0⊂Z. We suppose that F is bounded and the linear system is approximately controllable on [0,δ] for all δ∈(0,τ). Under these conditions, we prove the following statement: the semilinear impulsive evolution equation is approximately controllable on [0,τ].

Año de publicación:

2015

Keywords:

Fuente:

scopus

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