On two coupled degenerate parabolic equations motivated by thermodynamics
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2937 | |
dc.contributor.author | Mielke, Alexander | |
dc.date.accessioned | 2022-07-08T13:04:39Z | |
dc.date.available | 2022-07-08T13:04:39Z | |
dc.date.issued | 2022 | |
dc.description.abstract | We discuss a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to conservation of the total energy. The motivation of studying this system comes from Prandtl's and Kolmogorov's one and two-equation models for turbulence, where the energy-like variable is the mean turbulent kinetic energy. Because of the degeneracies there are solutions with time-dependent support like in the porous medium equation, which is contained in our system as a special case. The motion of the free boundary may be driven by either self-diffusion of the energy-like variable or by dissipation of the velocity-like variable. The cross-over of these two phenomena is exemplified for the associated planar traveling fronts. We provide existence of suitably defined weak and very weak solutions. After providing a thermodynamically motivated gradient structure we also establish convergence into steady state for bounded domains and provide a conjecture on the asymptotically self-similar behavior of the solutions in Rd for large times. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9695 | |
dc.identifier.uri | https://doi.org/10.34657/8733 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2937 | |
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 | Free boundary | eng |
dc.subject.other | growing support | eng |
dc.subject.other | gradient system | eng |
dc.subject.other | energy conservation | eng |
dc.subject.other | momentum conservation | eng |
dc.subject.other | porous medium equation | eng |
dc.subject.other | energy-dissipation estimates | eng |
dc.subject.other | entropy estimates | eng |
dc.title | On two coupled degenerate parabolic equations motivated by thermodynamics | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 44 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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