@Article{Kamont2014,
author = "Kamont, Zdzisław",
title = "Existence and regularity of solutions for hyperbolic functional differential problems",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "2",
pages = "217--242",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.2.217",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.2.217",
abstract = "A generalized Cauchy problem for quasilinear hyperbolic functional differential systems is considered. A theorem on the local existence of weak solutions is proved. The initial problem is transformed into a system of functional integral equations for an unknown function and for their partial derivatives with respect to spatial variables. The existence of solutions for this system is proved by using a method of successive approximations. We show a theorem on the differentiability of solutions with respect to initial functions which is the main result of the paper.",
keywords = "functional differential equations, weak solutions, Haar pyramid, differentiability with respect to initial functions",
issn = "1232-9274"
}