Ill-posed problems in thermomechanics

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DREHER, Michael, Ramón QUINTANILLA, Reinhard RACKE, 2009. Ill-posed problems in thermomechanics. In: Applied Mathematics Letters. Elsevier. 22(9), pp. 1374-1379. ISSN 0893-9659. eISSN 1873-5452. Available under: doi: 10.1016/j.aml.2009.03.010

@article{Dreher2009Illpo-58198, title={Ill-posed problems in thermomechanics}, year={2009}, doi={10.1016/j.aml.2009.03.010}, number={9}, volume={22}, issn={0893-9659}, journal={Applied Mathematics Letters}, pages={1374--1379}, author={Dreher, Michael and Quintanilla, Ramón and Racke, Reinhard} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Dreher, Michael</dc:creator> <dc:language>eng</dc:language> <dspace:isPartOfCollection rdf:resource=""/> <dcterms:isPartOf rdf:resource=""/> <dc:date rdf:datatype="">2022-07-28T08:26:35Z</dc:date> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Racke, Reinhard</dc:contributor> <bibo:uri rdf:resource=""/> <dcterms:issued>2009</dcterms:issued> <dc:contributor>Dreher, Michael</dc:contributor> <dc:creator>Quintanilla, Ramón</dc:creator> <dcterms:title>Ill-posed problems in thermomechanics</dcterms:title> <dc:creator>Racke, Reinhard</dc:creator> <dc:contributor>Quintanilla, Ramón</dc:contributor> <dcterms:available rdf:datatype="">2022-07-28T08:26:35Z</dcterms:available> <dcterms:abstract xml:lang="eng">Several thermomechanical models have been proposed from a heuristic point of view. A mathematical analysis should help to clarify the applicability of these models, among those recent thermal or viscoelastic models. Single-phase-lag and dual-phase-lag heat conduction models can be interpreted as formal expansions of delay equations. The delay equations are shown to be ill-posed, as are the formal expansions of higher order — in contrast to lower-order expansions leading to Fourier’s or Cattaneo’s law. The ill-posedness is proved, showing the lack of continuous dependence on the data, and thus showing that these models (delay or higher-order expansion ones) are highly explosive. In this note we shall present conditions for when this happens.</dcterms:abstract> </rdf:Description> </rdf:RDF>

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