Opuscula Math. 34, no. 2 (2014), 217-242

Opuscula Mathematica

Existence and regularity of solutions for hyperbolic functional differential problems

Zdzisław Kamont

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.

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  • Zdzisław Kamont
  • University of Gdansk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdansk, Poland
  • Received: 2013-03-25.
  • Revised: 2013-09-14.
  • Accepted: 2013-09-14.
Opuscula Mathematica - cover

Cite this article as:
Zdzisław Kamont, Existence and regularity of solutions for hyperbolic functional differential problems, Opuscula Math. 34, no. 2 (2014), 217-242, http://dx.doi.org/10.7494/OpMath.2014.34.2.217

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