# 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

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topLomtatidze, 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 -

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