Fredholm Solvability of Time-Periodic Boundary Value Hyperbolic Problems

2016/04/15 by Kmit, I., Klyuchnyk, R.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.04401

Abstract

We investigate a large class of linear boundary value problems for the general first-order one-dimensional hyperbolic systems in the strip [0,1]×\R. We state rather broad natural conditions on the data under which the operators of the problems satisfy the Fredholm alternative in the spaces of continuous and time-periodic functions. A crucial ingredient of our analysis is a non-resonance condition, which is formulated in terms of the data responsible for the bijective part of the Fredholm operator. In the case of 2× 2 systems with reflection boundary conditions, we provide a criterium for the non-resonant behavior of the system.

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