Differentiability with respect to initial functions of solutions to nonlinear hyperbolic functional differential systems

• Autores: Z. Kamont
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 65, Fasc. 3, 2014, págs. 379-405
• Idioma: inglés
• DOI: 10.1007/s13348-013-0098-z
• Enlaces
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• Resumen

  • A generalized Cauchy problem for nonlinear hyperbolic functional differential systems is considered. A theorem on the 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 of this system is proved by using a method of successive approximations. It is shown a result on the differentiability of solutions with respect to initial functions. This is the main result of the paper.

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