Geodesic
Inverse problems with pointwise overdetermination for some quasilinear parabolic systems
Matematičeskie trudy, Tome 22 (2019) no. 1, pp. 178-204

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

In the article, we examine well-posedness questions in the Sobolev spaces of the inverse source problem in the case of a quasilinear parabolic system of the second order. The main part of the operator is linear. The overdetermination conditions are values of a solution at some collection of interior points. It is demonstrated that, in the case of at most linear growth of the nonlinearity, there exists a unique global (in time) solution and the problem is well-posed in the Sobolev classes. The conditions on the data are minimal and the results are sharp. 
@article{MT_2019_22_1_a6,
     author = {S. G. Pyatkov and V. V. Rotko},
     title = {Inverse problems with pointwise overdetermination for some quasilinear parabolic systems},
     journal = {Matemati\v{c}eskie trudy},
     pages = {178--204},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2019_22_1_a6/}
}
TY  - JOUR
AU  - S. G. Pyatkov
AU  - V. V. Rotko
TI  - Inverse problems with pointwise overdetermination for some quasilinear parabolic systems
JO  - Matematičeskie trudy
PY  - 2019
SP  - 178
EP  - 204
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2019_22_1_a6/
LA  - ru
ID  - MT_2019_22_1_a6
ER  - 
%0 Journal Article
%A S. G. Pyatkov
%A V. V. Rotko
%T Inverse problems with pointwise overdetermination for some quasilinear parabolic systems
%J Matematičeskie trudy
%D 2019
%P 178-204
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2019_22_1_a6/
%G ru
%F MT_2019_22_1_a6
S. G. Pyatkov; V. V. Rotko. Inverse problems with pointwise overdetermination for some quasilinear parabolic systems. Matematičeskie trudy, Tome 22 (2019) no. 1, pp. 178-204. http://geodesic.mathdoc.fr/item/MT_2019_22_1_a6/