Opuscula Math. 35, no. 6 (2015), 915-933

Opuscula Mathematica

On the quasilinear Cauchy problem for a hyperbolic functional differential equation

Elżbieta Puźniakowska-Gałuch

Abstract. The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.

Keywords: functional differential equations, Haar pyramid, differentiability of solutions, Fredholm type of equation.

Mathematics Subject Classification: 35R10, 35F25, 35A05.

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  • Elżbieta Puźniakowska-Gałuch
  • University of Gdańsk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdańsk, Poland
  • Communicated by Mirosław Lachowicz.
  • Received: 2014-08-17.
  • Revised: 2014-11-03.
  • Accepted: 2014-11-04.
  • Published online: 2015-06-06.
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Cite this article as:
Elżbieta Puźniakowska-Gałuch, On the quasilinear Cauchy problem for a hyperbolic functional differential equation, Opuscula Math. 35, no. 6 (2015), 915-933, http://dx.doi.org/10.7494/OpMath.2015.35.6.915

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