Stabilität elastodynamischer Schockwellen
Stabilität elastodynamischer Schockwellen
Loading...
Date
2023
Authors
Schlipf, Markus
Editors
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
International patent number
Link to the license
EU project number
Project
Open Access publication
Collections
Title in another language
Publication type
Dissertation
Publication status
Published
Published in
Abstract
Summary in another language
In this dissertation we consider planar shock-waves both in isentropic gas dynamics and in elastodynamics in two space dimensions. In the theory of hyperbolic systems, shock-waves are represented by weak solutions to nonlinear systems of conservation laws, satisfying jump conditions on a smooth hypersurface as well as entropy conditions motivated by physics. Given a reference shock-solution of the conservation laws and a multidimensional perturbation of the initial data or a small wave impinging on the shock-front, one may ask for the stability of the shock, i.e. if the shock-structure persists under perturbation. Due to the fundamental work of A. Majda and A. M. Blokhin, the question regarding nonlinear stability can be answered by analyzing a stability function known as the Lopatinski-determinant.
Considering the equations of isentropic elastodynamics in eulerian coordinates, we aim to give explicit expressions of stability-separatrices using the Lopatinski-determinant. The latter equations are supplemented by additional divergence constraints allowing to write them as a symmetric hyperbolic system at the cost of losing the conservative form.
By considering the so-called beta-model which was firstly proposed by Barker, Monteiro & Zumbrun in 2021 for MHD-LAX-shocks, we are able to present for the first time an explicit expression of the Lopatinski-determinant for compressive LAX-shocks in isentropic inviscid elastodynamics for general deformations. And by monotonicity arguments on specific intervals a way to calculate the boundaries of the stability domains analytically.
Subject (DDC)
510 Mathematics
Keywords
Elastodynamik,LAX-Schocks,Strukturelle Stabilität,Lopatinski-Determinante
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690
SCHLIPF, Markus, 2023. Stabilität elastodynamischer Schockwellen [Dissertation]. Konstanz: University of KonstanzBibTex
@phdthesis{Schlipf2023Stabi-66050, year={2023}, title={Stabilität elastodynamischer Schockwellen}, author={Schlipf, Markus}, address={Konstanz}, school={Universität Konstanz} }
RDF
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/66050"> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:title>Stabilität elastodynamischer Schockwellen</dcterms:title> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-02-13T06:44:35Z</dcterms:available> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/66050/6/Schlipf_2-2jdfhnuzr67n4.pdf"/> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dc:contributor>Schlipf, Markus</dc:contributor> <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by-sa/4.0/"/> <dc:rights>Attribution-ShareAlike 4.0 International</dc:rights> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:creator>Schlipf, Markus</dc:creator> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/66050/6/Schlipf_2-2jdfhnuzr67n4.pdf"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2023-02-13T06:44:35Z</dc:date> <dcterms:issued>2023</dcterms:issued> <dc:language>deu</dc:language> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/66050"/> </rdf:Description> </rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Examination date of dissertation
February 1, 2023
University note
Konstanz, Univ., Doctoral dissertation, 2023