Geodesic
Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term
Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 273-290

Voir la notice de l'article provenant de la source Math-Net.Ru

In a Banach space $E$, we consider the inverse problem $du(t)/dt=Au(t)+\phi(t)p$, $u(0)=u_0$, $u(T)=u_1$, with an unknown function $u(t)$ and an element $p\in E$. The operator $A$ is assumed linear and closed. In this paper, we establish minimal constraints on the function $\phi\in C([0,T])$ for which the uniqueness of the solution of the inverse problem is completely described in terms of the eigenvalues of the operator $A$. 
@article{MZM_2005_77_2_a8,
     author = {I. V. Tikhonov and Yu. S. \`Eidel'man},
     title = {Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term},
     journal = {Matemati\v{c}eskie zametki},
     pages = {273--290},
     publisher = {mathdoc},
     volume = {77},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a8/}
}
TY  - JOUR
AU  - I. V. Tikhonov
AU  - Yu. S. Èidel'man
TI  - Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term
JO  - Matematičeskie zametki
PY  - 2005
SP  - 273
EP  - 290
VL  - 77
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a8/
LA  - ru
ID  - MZM_2005_77_2_a8
ER  - 
%0 Journal Article
%A I. V. Tikhonov
%A Yu. S. Èidel'man
%T Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term
%J Matematičeskie zametki
%D 2005
%P 273-290
%V 77
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a8/
%G ru
%F MZM_2005_77_2_a8
I. V. Tikhonov; Yu. S. Èidel'man. Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term. Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 273-290. http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a8/