• 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

    Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Type
    Article
    Authors
    Said-Houari, Belkacem
    Nascimento, Flávio A Falcão
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2012-09
    Permanent link to this record
    http://hdl.handle.net/10754/562313
    
    Metadata
    Show full item record
    Abstract
    The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.
    Citation
    Said-Houari, B., & Nascimento, F. A. F. (2012). Global existence and nonexistence for the viscoelastic wave equation with nonlinear boundary damping-source interaction. Communications on Pure and Applied Analysis, 12(1), 375–403. doi:10.3934/cpaa.2013.12.375
    Sponsors
    Doctorate student by State University of Maringa, partially supported by a grant of CNPq, BrazilThe authors thanks Prof. Marcelo Moreira Cavalcanti for many helpful comments, which improve the first version of this paper. Moreover, the first author thanks KAUST for its support.
    Publisher
    American Institute of Mathematical Sciences (AIMS)
    Journal
    Communications on Pure and Applied Analysis
    DOI
    10.3934/cpaa.2013.12.375
    ae974a485f413a2113503eed53cd6c53
    10.3934/cpaa.2013.12.375
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

    entitlement

     
    DSpace software copyright © 2002-2023  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.