• Login
    View Item 
    •   Home
    • Office of Sponsored Research (OSR)
    • KAUST Funded Research
    • Publications Acknowledging KAUST Support
    • View Item
    •   Home
    • Office of Sponsored Research (OSR)
    • KAUST Funded Research
    • Publications Acknowledging KAUST Support
    • 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

    Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Type
    Article
    Authors
    Blanchet, Adrien
    Carrillo, Jose A.
    Laurencot, Philippe
    Date
    2009
    Permanent link to this record
    http://hdl.handle.net/10754/671195
    
    Metadata
    Show full item record
    Abstract
    This paper is devoted to the analysis of non-negative solutions for a generalisation of the classical parabolic-elliptic Patlak-Keller-Segel system with d 3 and porous medium-like non-linear diffusion. Here, the non-linear diffusion is chosen in such a way that its scaling and the one of the Poisson term coincide. We exhibit that the qualitative behaviour of solutions is decided by the initial mass of the system. Actually, there is a sharp critical mass M c such that if M in (0, M-c] solutions exist globally in time, whereas there are blowing-up solutions otherwise. We also show the existence of self-similar solutions for M in (0, M-c). While characterising the possible infinite time blowing-up profile for M = M c , we observe that the long time asymptotics are much more complicated than in the classical Patlak-Keller-Segel system in dimension two. © 2008 Springer-Verlag.
    Citation
    Blanchet, A., Carrillo, J. A., & Laurençot, P. (2008). Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions. Calculus of Variations and Partial Differential Equations, 35(2), 133–168. doi:10.1007/s00526-008-0200-7
    Sponsors
    KAUST investigator award.
    Publisher
    Springer Science and Business Media LLC
    Journal
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
    DOI
    10.1007/s00526-008-0200-7
    arXiv
    0801.2310
    Additional Links
    http://link.springer.com/10.1007/s00526-008-0200-7
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00526-008-0200-7
    Scopus Count
    Collections
    Publications Acknowledging KAUST Support

    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.