• Login
    View Item 
    •   Home
    • Research
    • Articles
    • View Item
    •   Home
    • Research
    • Articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguideTheses and Dissertations LibguideSubmit an Item

    Statistics

    Display statistics

    Decay to Equilibrium for Energy-Reaction-Diffusion Systems

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    16m1062065.pdf
    Size:
    563.2Kb
    Format:
    PDF
    Description:
    Published version
    Download
    Type
    Article
    Authors
    Haskovec, Jan cc
    Hittmeir, Sabine
    Markowich, Peter A. cc
    Mielke, Alexander
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    KAUST Grant Number
    1000000193
    Date
    2018-02-06
    Online Publication Date
    2018-02-06
    Print Publication Date
    2018-01
    Permanent link to this record
    http://hdl.handle.net/10754/627362
    
    Metadata
    Show full item record
    Abstract
    We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.
    Citation
    Haskovec J, Hittmeir S, Markowich P, Mielke A (2018) Decay to Equilibrium for Energy-Reaction-Diffusion Systems. SIAM Journal on Mathematical Analysis 50: 1037–1075. Available: http://dx.doi.org/10.1137/16M1062065.
    Sponsors
    The work of the first and third authors was supported by KAUST baseline funds and grant 1000000193. The work of the second author was supported by the Austrian Science Fund via the Hertha-Firnberg project T-764, and the previous funding by the Austrian Academy of Sciences ÖAW via the New Frontiers project NST-000. The work of the fourth author was partially supported by Einstein-Stiftung Berlin through the Matheon-Project OT1.
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Mathematical Analysis
    DOI
    10.1137/16M1062065
    Additional Links
    https://epubs.siam.org/doi/10.1137/16M1062065
    ae974a485f413a2113503eed53cd6c53
    10.1137/16M1062065
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2022  DuraSpace
    Quick Guide | Contact Us | KAUST University Library
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.