Linear Hyperbolic Systems on Networks: well-posedness and qualitative properties

Marjeta Kramar, Delio Mugnolo, Serge Nicaise
2020 E S A I M: Control, Optimisation and Calculus of Variations  
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
more » ... y 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 . p, li { white-space: pre-wrap; }
doi:10.1051/cocv/2020091 fatcat:xl6etajj6vftfknaebxcsxt2ke