Geodesic
On the Cauchy problem for linear hyperbolic functional-differential equations
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 391-440 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing literature.
We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing literature.
DOI : 10.1007/s10587-012-0037-2
Classification : 35A01, 35A02, 35B30, 35L10, 35L15
Keywords: functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness; existence of solutions 
@article{10_1007_s10587_012_0037_2,
     author = {Lomtatidze, Alexander and \v{S}remr, Ji\v{r}{\'\i}},
     title = {On the {Cauchy} problem for linear hyperbolic functional-differential equations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {391--440},
     year = {2012},
     volume = {62},
     number = {2},
     doi = {10.1007/s10587-012-0037-2},
     mrnumber = {2990184},
     zbl = {1265.35195},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0037-2/}
}
TY  - JOUR
AU  - Lomtatidze, Alexander
AU  - Šremr, Jiří
TI  - On the Cauchy problem for linear hyperbolic functional-differential equations
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 391
EP  - 440
VL  - 62
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0037-2/
DO  - 10.1007/s10587-012-0037-2
LA  - en
ID  - 10_1007_s10587_012_0037_2
ER  - 
%0 Journal Article
%A Lomtatidze, Alexander
%A Šremr, Jiří
%T On the Cauchy problem for linear hyperbolic functional-differential equations
%J Czechoslovak Mathematical Journal
%D 2012
%P 391-440
%V 62
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-012-0037-2/
%R 10.1007/s10587-012-0037-2
%G en
%F 10_1007_s10587_012_0037_2
Lomtatidze, Alexander; Šremr, Jiří. On the Cauchy problem for linear hyperbolic functional-differential equations. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 391-440. doi: 10.1007/s10587-012-0037-2

Cité par Sources :