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Ukrainian Mathematical Journal

, Volume 65, Issue 2, pp 260–276 | Cite as

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

  • I. Ya. Kmit
  • L. Recke
  • V. I. Tkachenko
Article

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.

Keywords

Hyperbolic System Evolution Operator Continuous Solution Exponential Dichotomy Nonlocal Boundary Condition 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • I. Ya. Kmit
    • 1
    • 2
  • L. Recke
    • 2
  • V. I. Tkachenko
    • 3
  1. 1.Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine
  2. 2.Humboldt UniversityBerlinGermany
  3. 3.Institute of Mathematics of National Academy of Sciences of UkraineKyivUkraine

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