Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems
Please always quote using this URN:urn:nbn:de:0296-matheon-3542
- 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. The main tools of the proofs are separation of variables, integral representation of the solutions of the corresponding boundary value problems of the ODE systems and an abstract criterion for Fredholmness which seems to be new.
Author: | Irina Kmit, Lutz Recke |
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URN: | urn:nbn:de:0296-matheon-3542 |
Referee: | Jürgen Sprekels |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2006/08/30 |
Release Date: | 2006/08/30 |
Tag: | |
Institute: | Humboldt-Universität zu Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B10 Periodic solutions |
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L50 Initial-boundary value problems for first-order hyperbolic systems | |
47-XX OPERATOR THEORY / 47Axx General theory of linear operators / 47A53 (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] | |
Preprint Number: | 342 |