On the Cauchy problem for linear hyperbolic functional-differential equations
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 391-440.
Voir la notice de l'article dans Czech Digital Mathematics Library
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
Mots-clés : functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness; existence of solutions
Mots-clés : 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}, publisher = {mathdoc}, volume = {62}, number = {2}, year = {2012}, doi = {10.1007/s10587-012-0037-2}, mrnumber = {2990184}, zbl = {1265.35195}, language = {en}, url = {https://geodesic-test.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 PB - mathdoc UR - https://geodesic-test.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 %I mathdoc %U https://geodesic-test.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. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0037-2/
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