On the Cauchy problem for linear hyperbolic functional-differential equations

Alexander Lomtatidze; Jiří Šremr

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 2, page 391-440
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Lomtatidze, Alexander, and Šremr, Jiří. "On the Cauchy problem for linear hyperbolic functional-differential equations." Czechoslovak Mathematical Journal 62.2 (2012): 391-440. <http://eudml.org/doc/246271>.

@article{Lomtatidze2012,
abstract = {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.},
author = {Lomtatidze, Alexander, Šremr, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness; existence of solutions; functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness},
language = {eng},
number = {2},
pages = {391-440},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the Cauchy problem for linear hyperbolic functional-differential equations},
url = {http://eudml.org/doc/246271},
volume = {62},
year = {2012},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 391
EP - 440
AB - 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.
LA - eng
KW - functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness; existence of solutions; functional-differential equation of hyperbolic type; Cauchy problem; Fredholm alternative; well-posedness
UR - http://eudml.org/doc/246271
ER -

References

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