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

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

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.

• Language: English
• Keywords: hyperbolic systems, operator semigroups, PDEs on networks, invariance properties, Saint-Venant system, second sound
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 46 str.
• Numbering: Vol. 27, art. 7
• PID: 20.500.12556/RUL-125104
• UDC: 51
• ISSN on article: 1292-8119
• DOI: 10.1051/cocv/2020091
• COBISS.SI-ID: 51482883
• Publication date in RUL: 04.03.2021

Record is a part of a journal

• Title: ESAIM
• Shortened title: ESAIM, COCV
• Publisher: EDP Sciences, Société de Mathématiques Appliquées et Industrielles
• ISSN: 1292-8119
• COBISS.SI-ID: 513891097

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: akademska matematika, hiperbolični sistemi, operatorske polgrupe, PDE na omrežjih, invariantne lastnosti, Saint-Venantovi sistemi, drugi zvok