Geodesic
An approach to solving an ill-posed problem for a nonlinear differential equation
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 231-237

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

A reverse time problem is considered for a semilinear differential equation. We suggest an approach to construct approximate solving methods for the problem under study. The approach generalizes the scheme proposed by A. B. Bakushinskii for linear ill-posed problems. Two-sided error estimates for the proposed methods are obtained via the error estimates for the corresponding linear problem on standard correctness classes. Order optimality is proved for the considered algorithms.
Keywords: differential equation; inverse problem; modulus of continuity of the inverse operator; approximate method; error estimate. 
@article{TIMM_2015_21_1_a23,
     author = {E. V. Tabarintseva},
     title = {An approach to solving an ill-posed problem for a nonlinear differential equation},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {231--237},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a23/}
}
TY  - JOUR
AU  - E. V. Tabarintseva
TI  - An approach to solving an ill-posed problem for a nonlinear differential equation
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2015
SP  - 231
EP  - 237
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a23/
LA  - ru
ID  - TIMM_2015_21_1_a23
ER  - 
%0 Journal Article
%A E. V. Tabarintseva
%T An approach to solving an ill-posed problem for a nonlinear differential equation
%J Trudy Instituta matematiki i mehaniki
%D 2015
%P 231-237
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a23/
%G ru
%F TIMM_2015_21_1_a23
E. V. Tabarintseva. An approach to solving an ill-posed problem for a nonlinear differential equation. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 231-237. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a23/