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arXiv · 2003.08281

Linear Hyperbolic Systems on Networks

Marjeta Kramar Fijavž·Delio Mugnolo·Serge Nicaise
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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.

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Marjeta Kramar Fijavž, Delio Mugnolo, Serge Nicaise. 2020-12-19. Linear Hyperbolic Systems on Networks. https://doi.org/10.1051/cocv%2F2020091

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