Affiliation:
1. Siberian Federal University , Svobodnii Str. 79, 660041 Krasnoyarsk , Russia
Abstract
Abstract
We establish the stabilization of the strong solution
(
u
(
t
,
x
)
,
k
(
t
)
)
{(u(t,x),k(t))}
to the inverse problem for a pseudoparabolic equation
(
u
+
η
M
u
)
t
+
M
u
+
k
(
t
)
u
=
f
{(u+\eta Mu)_{t}+Mu+k(t)u=f}
with an unknown coefficient
k
(
t
)
{k(t)}
to the solution
(
u
∞
,
k
∞
)
{(u^{\infty},k^{\infty})}
of the appropriate stationary inverse problem. The operator
M
=
-
div
(
ℳ
(
x
)
∇
)
+
m
(
x
)
I
{M=-\operatorname{div}(\mathcal{M}(x)\nabla)+m(x)I}
is supposed to be elliptic and self-adjoint. The asymptotic behavior of the solution
(
u
(
t
,
x
)
,
k
(
t
)
)
{(u(t,x),k(t))}
is investigated as
t
→
+
∞
{t\to+\infty}
.
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