Geodesic
The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane
Matematičeskie zametki, Tome 107 (2020) no. 1, pp. 74-86

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

We prove existence and uniqueness theorems for the solution of the inverse problem of simultaneous determination of the $t$-dependent coefficients of $u$ and $u_x$ in a nondivergent parabolic equation with two independent variables from integral observation of $x$. Estimates of the maxima of the moduli of these coefficients with constants explicitly expressed in terms of the input data of the problem are given. An example of an inverse problem to which the proved theorems apply is presented.
Keywords: inverse problem, integral observation.
Mots-clés : parabolic equations 
@article{MZM_2020_107_1_a6,
     author = {V. L. Kamynin},
     title = {The {Inverse} {Problem} of {Simultaneous} {Determination} of the {Two} {Time-Dependent} {Lower} {Coefficients} in a {Nondivergent} {Parabolic} {Equation} in the {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {74--86},
     publisher = {mathdoc},
     volume = {107},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_1_a6/}
}
TY  - JOUR
AU  - V. L. Kamynin
TI  - The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane
JO  - Matematičeskie zametki
PY  - 2020
SP  - 74
EP  - 86
VL  - 107
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2020_107_1_a6/
LA  - ru
ID  - MZM_2020_107_1_a6
ER  - 
%0 Journal Article
%A V. L. Kamynin
%T The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane
%J Matematičeskie zametki
%D 2020
%P 74-86
%V 107
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2020_107_1_a6/
%G ru
%F MZM_2020_107_1_a6
V. L. Kamynin. The Inverse Problem of Simultaneous Determination of the Two Time-Dependent Lower Coefficients in a Nondivergent Parabolic Equation in the Plane. Matematičeskie zametki, Tome 107 (2020) no. 1, pp. 74-86. http://geodesic.mathdoc.fr/item/MZM_2020_107_1_a6/