Opuscula Math. 34, no. 2 (2014), 217-242
Existence and regularity of solutions for hyperbolic functional differential problems
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.
Mathematics Subject Classification: 35R10, 35L60.
- Received: 2013-03-25.
- Revised: 2013-09-14.
- Accepted: 2013-09-14.