I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1998, VOLUME 4, NUMBER 2, PAGES 691-708
On the solvability of linear inverse problem with final
overdetermination in a Banach space
I. V. Tikhonov
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we consider the inverse problem in a Banach space
where the element is unknown.
Our main result may be written as follows: Let
and let be
the infinitesimal generator of a semigroup
be defined by
Suppose that , and -.
Then for each pair the inverse problem has a unique solution
, i. e., there exists a unique such that the corresponding function
satisfies the final condition .
Moreover, with the
constant computing in the explicit form.
To illustrate the results we present three examples: the linear
inhomogeneous system of ODE, the heat equation in , and the
one-dimensional "transport equation".
All articles are
published in Russian.
Last modified: June 17, 1998