Fredholm alternative for periodic-Dirichlet problems for linear hyperbolic systems |
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Authors: | Irina Kmit |
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Institution: | a Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova St. 3b, 79060 Lviv, Ukraine b Institute of Mathematics, Humboldt University of Berlin, Rudower Chaussee 25, 12489 Berlin, Germany |
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Abstract: | This paper concerns hyperbolic systems of two linear first-order PDEs in one space dimension with periodicity conditions in time and reflection boundary conditions in space. The coefficients of the PDEs are supposed to be time independent, but allowed to be discontinuous with respect to the space variable. We construct two scales of Banach spaces (for the solutions and for the right-hand sides of the equations, respectively) such that the problem can be modeled by means of Fredholm operators of index zero between corresponding spaces of the two scales. |
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Keywords: | No small denominators Anisotropic Sobolev spaces Reflection boundary conditions Possibly discontinuous coefficients |
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