Geodesic
Localization for the discontinuity line of the right-hand side of a~differential equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 62-72

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

We propose a new approach to the study of inverse problems for differential equations with constant coefficients. Its application is illustrated by the example of one partial differential equation with three independent variables. The right-hand side of the equation is assumed to be a discontinuous function of space variables. The inverse problem is to find some hull containing the discontinuity line of the right-hand side. An algorithm for constructing such a hull is obtained: it is a square whose sides are tangent to the discontinuity line.
Keywords: inverse problem, discontinuous function, weak solution, differential properties. 
@article{SJIM_2016_19_1_a5,
     author = {D. S. Konovalova},
     title = {Localization for the discontinuity line of the right-hand side of a~differential equation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {62--72},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a5/}
}
TY  - JOUR
AU  - D. S. Konovalova
TI  - Localization for the discontinuity line of the right-hand side of a~differential equation
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2016
SP  - 62
EP  - 72
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a5/
LA  - ru
ID  - SJIM_2016_19_1_a5
ER  - 
%0 Journal Article
%A D. S. Konovalova
%T Localization for the discontinuity line of the right-hand side of a~differential equation
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2016
%P 62-72
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a5/
%G ru
%F SJIM_2016_19_1_a5
D. S. Konovalova. Localization for the discontinuity line of the right-hand side of a~differential equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 19 (2016) no. 1, pp. 62-72. http://geodesic.mathdoc.fr/item/SJIM_2016_19_1_a5/