Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities : dedicated to Peter Markowich on the occasion of his sixtieth birthday
dc.bibliographicCitation.volume | 2349 | |
dc.contributor.author | Mielke, Alexander | |
dc.contributor.author | Mittnenzweig, Markus | |
dc.date.accessioned | 2017-03-29T23:50:34Z | |
dc.date.available | 2019-06-28T08:05:08Z | |
dc.date.issued | 2016 | |
dc.description.abstract | We discuss how the recently developed energy-dissipation methods for reaction-diffusion systems can be generalized to the non-isothermal case. For this we use concave entropies in terms of the densities of the species and the internal energy, with the important feature, that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2162 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2274 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.ispartofseries | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2349, ISSN 2198-5855 | eng |
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 | Energy-reaction-diffusion systems | eng |
dc.subject | vector-valued inequalities | eng |
dc.subject | cross diffusion | eng |
dc.subject | log-Sobolev inequality | eng |
dc.subject | entropy functional | eng |
dc.subject | exponential decay of relative entropy | eng |
dc.subject | convexity method | eng |
dc.subject.ddc | 510 | eng |
dc.title | Convergence to equilibrium in energy-reaction-diffusion systems using vector-valued functional inequalities : dedicated to Peter Markowich on the occasion of his sixtieth birthday | eng |
dc.type | report | eng |
dc.type | Text | eng |
dcterms.bibliographicCitation.journalTitle | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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