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)
4.2 Approximate Controllability
Now, we are ready to formulate and prove the main
result of the this section, which is the approximate
of the semilinear impulsive wave equation with
bounded nonlinear perturbation.
THEOREM 4.1. The semilinear wave equation
(15) with impulses and delays is approximately
controllable on [0,τ].
Proof. From Larez et al. (2011), we know that the
corresponding linear system without impulses
(
z
0
= Az + Bu, z ∈ Z
1/2
, t ∈ (0,τ];
z(0) = z
0
,
(29)
is controllable on [τ − δ,τ] for all 0 < δ < τ. On
the other hand, the hypothesis (H1) and (H2) in
Theorem 3.1 are satisfied, and we get the result.
5 Final Remark
This technique can be applied to those systems
where the linear part does not generate a compact
semigroup, are controllable on any [0,δ] for δ >
0, and the nonlinear perturbation is bounded. An
example of such systems is the following controlled
thermoelastic plate equation whose linear part was
studied in Larez et al. (2011).
y
tt
+ ∆
2
y + α∆θ
=u
1
(t,x) + f
1
(t,y,y
t
,θ, u(t)),
on (0,τ) × Ω,
θ
t
− β∆θ − α∆y
t
= u
2
(t,x) + f
2
(t,y,y
t
,θ, u(t)),
on (0,τ) × Ω,
θ = y = ∆y = 0, on (0,τ) × ∂Ω,
y
t
(t
+
k
,x) =
y
t
(t
−
k
,x)
+ I
1
k
(t,y(t
k
,x),y
t
(t
k
,x),u(t
k
,x)),
x ∈ Ω,
θ(t
+
k
,x) =
θ(t
−
k
,x)+I
2
k
(t
k
,θ(t
k
,x),u(t
k
,x)),
x ∈ Ω,
(30)
in the space Z = X
1
× X × X, where Ω is a
bounded domain in R
n
, the distributed controls
u
1
,u
2
∈ L
2
([0,τ]; L
2
(Ω)) and I
i
k
, f
i
are smooth
functions with f
i
,i = 1, 2 bounded. Of course,
for finite-dimensional control systems, all these
results are valid for exact controllability; so from
the point of view of applications, we can study
real life control systems governed by ordinary
differential equations in finite-dimensional spaces,
with impulses and delays.
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http://novasinergia.unach.edu.ec 43