TY  - JOUR
ID  - Sapa2015
LB  - Sapa2015
AU  - Sapa, Lucjan
TI  - Existence, uniqueness and estimates of classical solutions to some evolutionary system
ST  - Existence, uniqueness and estimates of classical solutions to some evolutionary system
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 6
SP  - 935
EP  - 956
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.6.935
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.6.935
AB  - The theorem of the local existence, uniqueness and estimates of solutions in Hölder spaces for some nonlinear differential evolutionary system with initial conditions is formulated and proved. This system is composed of one partial hyperbolic second-order equation and an ordinary subsystem with a parameter. In the proof of the theorem we use the Banach fixed-point theorem, the Arzeli-Ascola lemma and the integral form of the differential problem.
KW  - hyperbolic wave equation
KW  - telegraph equation
KW  - system of nonlinear equations
KW  - existence, uniqueness and estimates of solutions
KW  - Hölder space
SN  - 1232-9274
ER  -