Author:
Ashurov Ravshan,Shakarova Marjona
Abstract
UDC 517.9
We consider a Schrödinger equation
i
∂
t
ρ
u
(
x
,
t
)
-
u
x
x
(
x
,
t
)
=
p
(
t
)
q
(
x
)
+
f
(
x
,
t
)
,
0
<
t
≤
T
,
0
<
ρ
<
1
,
with the Riemann–Liouville derivative. An inverse problem is investigated in which, parallel with
u
(
x
,
t
)
,
a time-dependent factor
p
(
t
)
of the source function is also unknown. To solve this inverse problem, we use an additional condition
B
[
u
(
⋅
,
t
)
]
=
ψ
(
t
)
with an arbitrary bounded linear functional
B
. The existence and uniqueness theorem for the solution to the problem under consideration is proved. The stability inequalities are obtained. The applied method make it possible to study a similar problem by taking, instead of
d
2
/
d
x
2
,
an arbitrary elliptic differential operator
A
(
x
,
D
)
with compact inverse.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science