Opuscula Math. 35, no. 6 (2015), 935-956

Opuscula Mathematica

Existence, uniqueness and estimates of classical solutions to some evolutionary system

Lucjan Sapa

Abstract. The theorem of the local existence, uniqueness and estimates of solutions in Hölder spaces for some nonlinear differential evolutionary system with initial conditions is formulated and proved. This system is composed of one partial hyperbolic second-order equation and an ordinary subsystem with a parameter. In the proof of the theorem we use the Banach fixed-point theorem, the Arzeli-Ascola lemma and the integral form of the differential problem.

Keywords: hyperbolic wave equation, telegraph equation, system of nonlinear equations, existence, uniqueness and estimates of solutions, Hölder space.

Mathematics Subject Classification: 35M31, 35A09, 35A01, 35A02, 35B45.

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  • Lucjan Sapa
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
  • Communicated by Mirosław Lachowicz.
  • Received: 2014-05-12.
  • Revised: 2015-02-12.
  • Accepted: 2015-02-16.
  • Published online: 2015-06-06.
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Cite this article as:
Lucjan Sapa, Existence, uniqueness and estimates of classical solutions to some evolutionary system, Opuscula Math. 35, no. 6 (2015), 935-956, http://dx.doi.org/10.7494/OpMath.2015.35.6.935

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