Geodesic
Stability estimates in identification problems for the convection-diffusion-reaction equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2190-2205

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

Identification problems for the stationary convection-diffusion-reaction equation in a bounded domain with a Dirichlet condition imposed on the boundary of the domain are studied. By applying an optimization method, these problems are reduced to inverse extremum problems in which the variable diffusivity and the volume density of substance sources are used as control functions. Their solvability is proved for an arbitrary weakly lower semicontinuous cost functional and particular cost functionals. An analysis of the optimality system is used to establish sufficient conditions on the input data under which the solutions of particular extremum problems are unique and stable with respect to small perturbations in the cost functional and in one of the functions involved in the boundary value problem. 
@article{ZVMMF_2012_52_12_a6,
     author = {G. V. Alekseev and I. S. Vakhitov and O. V. Soboleva},
     title = {Stability estimates in identification problems for the convection-diffusion-reaction equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2190--2205},
     publisher = {mathdoc},
     volume = {52},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a6/}
}
TY  - JOUR
AU  - G. V. Alekseev
AU  - I. S. Vakhitov
AU  - O. V. Soboleva
TI  - Stability estimates in identification problems for the convection-diffusion-reaction equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 2190
EP  - 2205
VL  - 52
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a6/
LA  - ru
ID  - ZVMMF_2012_52_12_a6
ER  - 
%0 Journal Article
%A G. V. Alekseev
%A I. S. Vakhitov
%A O. V. Soboleva
%T Stability estimates in identification problems for the convection-diffusion-reaction equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 2190-2205
%V 52
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a6/
%G ru
%F ZVMMF_2012_52_12_a6
G. V. Alekseev; I. S. Vakhitov; O. V. Soboleva. Stability estimates in identification problems for the convection-diffusion-reaction equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 12, pp. 2190-2205. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_12_a6/