Hybrid dynamics comprising modes governed by partial differential equations [Elektronische Ressource] : modeling, analysis and control for semilinear hyperbolic systems in one space dimension / vorgelgt von Falk Michael Hante

Description

Hybrid Dynamics Comprising Modes Governed byPartial Differential Equations:Modeling, Analysis and Control for SemilinearHyperbolic Systems in One Space DimensionDer Naturwissenschaftlichen Fakulta¨tder Friedrich-Alexander-Universita¨t Erlangen-Nu¨rnbergzurErlangung des Doktorgrades Dr. rer. nat.vorgelegt vonFalk Michael Hanteaus DattelnAls Dissertation genehmigt von der Naturwissen-schaftlichen Fakulta¨t der Friedrich-Alexander-Universita¨tErlangen-Nu¨rnbergTag der mu¨ndlichen Pru¨fung: 14. Juli 2010Vorsitzender derPromotionskommission: Prof. Dr. Eberhard Ba¨nschErstberichterstatter/in: Prof. Dr. Gu¨nter LeugeringZweitberichterstatter/in: Prof. Dr. Hans Josef PeschAbstractHybrid dynamical systems are considered as a design paradigm or multiscale modelfor networked transport problems. Evolution in time is governed by switching amonga family of solutions to vector-valued, semi-linear hyperbolic partial differential equa-tions on a bounded interval in space with reflecting boundary conditions. Existence ofgeneralized solutions and appropriate continuous dependency properties are studiedon the discrete-continuous level. In particular, it is shown how the Zeno phenomenoncan be avoided, despite the propagation of discontinuities along characteristics re-sulting from instantanously changing boundary conditions and their interaction withswitching rules evaluating pointwise boundary obervation.

Sujets

• Mathematics

Informations

• Publié par: friedrich-alexander-universitat_erlangen-nurnberg
• Publié le: 01 janvier 2010
• Nombre de lectures: 7
• Langue: English

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