Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems

Details Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems Fredholm Alternative for Periodic-Dirichlet Problems for Linear Hyperbolic Systems

2006-08-18

arxiv.org/abs/math/0608461v2

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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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