Abstract
The paper deals with a generalized Cauchy problem for quasi-linear hyperbolic functional differential systems. The unknown function is the functional variable in the system of equations and the partial derivatives appear in the classical sense. A theorem on the local existence of a solution 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. A method of bicharacteristics and integral inequalites are applied.
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Kamont, Z. Classical solutions of hyperbolic functional differential systems. Acta Math Hung 124, 301–319 (2009). https://doi.org/10.1007/s10474-009-8189-8
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DOI: https://doi.org/10.1007/s10474-009-8189-8