Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2671 | |
dc.contributor.author | Hömberg, Dietmar | |
dc.contributor.author | Lasarzik, Robert | |
dc.date.accessioned | 2022-06-23T14:49:33Z | |
dc.date.available | 2022-06-23T14:49:33Z | |
dc.date.issued | 2019 | |
dc.description.abstract | In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ODE for the different phases of steel, and Maxwell's equations in a potential formulation. The existence of weak entropy solutions is shown by a suitable regularization and discretization technique. Moreover, we prove the weak-strong uniqueness of these solutions, i.e., that a weak entropy solutions coincides with a classical solution emanating form the same initial data as long as the classical one exists. The weak entropy solution concept has advantages in comparison to the previously introduced weak solutions, e.g., it allows to include free energy functions with low regularity properties corresponding to phase transitions. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9255 | |
dc.identifier.uri | https://doi.org/10.34657/8293 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2671 | |
dc.relation.hasversion | https://doi.org/10.1142/S021820252150041X | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Induction hardening | eng |
dc.subject.other | existence | eng |
dc.subject.other | weak-strong uniqueness | eng |
dc.subject.other | weak-entropy solution | eng |
dc.title | Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 36 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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