TY  - JOUR
ID  - Kamont2014
LB  - Kamont2014
AU  - Kamont, Zdzisław
TI  - Existence and regularity of solutions for hyperbolic functional differential problems
ST  - Existence and regularity of solutions for hyperbolic functional differential problems
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 2
SP  - 217
EP  - 242
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.2.217
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.2.217
AB  - 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.
KW  - functional differential equations
KW  - weak solutions
KW  - Haar pyramid
KW  - differentiability with respect to initial functions
SN  - 1232-9274
ER  -