Linear Hyperbolic Systems on Networks
Analysis of PDEs
2021-01-19 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks, can be reformulated in our rather flexible formalism, which generalizes the classical technique of first-order reduction. We study forward and backward well-posedness; furthermore, we provide necessary and sufficient conditions on both the boundary conditions and the coefficients arising in the first-order reduction for a given subset of the relevant ambient space to be invariant under the flow that governs the system. Several examples are studied.
Keywords
Cite
@article{arxiv.2003.08281,
title = {Linear Hyperbolic Systems on Networks},
author = {Marjeta Kramar Fijavž and Delio Mugnolo and Serge Nicaise},
journal= {arXiv preprint arXiv:2003.08281},
year = {2021}
}