Geodesic
Cauchy problem for a differential equation with piecewise smooth characteristics
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 3, pp. 3-19 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Cauchy problem is considered for an equation with first order partial derivatives and two independent variables. One of the coefficients multiplied by a partial derivative is assumed to be discontinuous. Therefore characteristics are proved to be piecewise smooth lines and hence the generalized solution of the Cauchy problem have specific properties. In particular, it is discontinuous in a certain domain and indefinite in another domain. Importance of such investigations is connected with possible applications of results in theory of probing.
Keywords: differential equations, Cauchy problem, discontinuous coefficients, uniqueness, probing.
Mots-clés : existence 
@article{VNGU_2018_18_3_a0,
     author = {D. S. Anikonov and D. S. Konovalova},
     title = {Cauchy problem for a differential equation with piecewise smooth characteristics},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {3--19},
     year = {2018},
     volume = {18},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a0/}
}
TY  - JOUR
AU  - D. S. Anikonov
AU  - D. S. Konovalova
TI  - Cauchy problem for a differential equation with piecewise smooth characteristics
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2018
SP  - 3
EP  - 19
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a0/
LA  - ru
ID  - VNGU_2018_18_3_a0
ER  - 
%0 Journal Article
%A D. S. Anikonov
%A D. S. Konovalova
%T Cauchy problem for a differential equation with piecewise smooth characteristics
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2018
%P 3-19
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a0/
%G ru
%F VNGU_2018_18_3_a0
D. S. Anikonov; D. S. Konovalova. Cauchy problem for a differential equation with piecewise smooth characteristics. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 3, pp. 3-19. http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a0/