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Robustness of the exponential dichotomies of boundary-value problems for the general first-order hyperbolic systems

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Ukrainian Mathematical Journal Aims and scope

We examine the robustness of exponential dichotomies of boundary-value problems for general linear first-order one-dimensional hyperbolic systems. It is assumed that the boundary conditions guarantee an increase in the smoothness of solutions in a finite time interval, including the reflection boundary conditions. We show that the dichotomy survives in the space of continuous functions under small perturbations of all coefficients in the differential equations.

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Authors and Affiliations

  1. Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    I. Ya. Kmit

  2. Humboldt University, Berlin, Germany

    I. Ya. Kmit & L. Recke

  3. Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. I. Tkachenko

Authors
  1. I. Ya. Kmit
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  2. L. Recke
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  3. V. I. Tkachenko
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 2, pp. 236–251, February, 2013.

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Kmit, I.Y., Recke, L. & Tkachenko, V.I. Robustness of the exponential dichotomies of boundary-value problems for the general first-order hyperbolic systems. Ukr Math J 65, 260–276 (2013). https://doi.org/10.1007/s11253-013-0776-8

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  • DOI: https://doi.org/10.1007/s11253-013-0776-8

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