Linear hyperbolic systems on networks: well-posedness and qualitative properties

Marjeta Kramar Fijavž , Delio Mugnolo , Serge Nicaise (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

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.

Mots clés: Hyperbolic systems; operator semigroups; PDEs on networks; invariance properties; Saint-Venant system; second sound

Domaines: Mathématiques [math]

Marjeta Kramar Fijavž, Delio Mugnolo, Serge Nicaise. Linear hyperbolic systems on networks: well-posedness and qualitative properties. ESAIM: Control, Optimisation and Calculus of Variations, 2021, 27, pp.7. ⟨10.1051/cocv/2020091⟩. ⟨hal-03158486⟩