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Existence of smooth shock profiles for hyperbolic systems with relaxation

Dressel, Alexander

German Title: Existenz von Schockprofilen fuer hyperbolische Systeme mit Relaxation

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Abstract

The aim of this thesis is the proof of the existence of relaxation shock profiles. The existence results apply if the reduced system is strictly hyperbolic and if the underlying hyperbolic system with relaxation fulfills easy-to-check sructural conditions. In general, the ODE system for the relaxation shock profile has a singular right-hand-side. The structural conditions allow the construction of a locally invariant manifold M, where the vector field to this ODE system has a smooth extenstion from a dense subset of M throughout M and the classical center manifold theorem applies. We apply our results to exponentially based moment closure systems.

Item Type: Dissertation
Supervisor: Jaeger, Willi
Date of thesis defense: 25 October 2005
Date Deposited: 16 Nov 2005 12:48
Date: 2005
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Hyperbolische Differentialgleichung, Relaxation, Verzweigung <Mathematik>
Uncontrolled Keywords: hyperbolic systems , relaxation , bifurcation
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