IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2014y2014i1n450289.html

Stochastic Viscoelastic Wave Equations with Nonlinear Damping and Source Terms

Author

Listed:
  • Shuilin Cheng
  • Yantao Guo
  • Yanbin Tang

Abstract

The goal of this paper is to study an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and source terms. Under certain conditions on the initial data: the relaxation function, the indices of nonlinear damping, and source terms and the random force, we prove the local existence and uniqueness of solution by the Galerkin approximation method. Then, considering the relationship between the indices of nonlinear damping and nonlinear source, we give the necessary conditions of global existence and explosion in finite time in some sense of solutions, respectively.

Suggested Citation

  • Shuilin Cheng & Yantao Guo & Yanbin Tang, 2014. "Stochastic Viscoelastic Wave Equations with Nonlinear Damping and Source Terms," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:450289
    DOI: 10.1155/2014/450289
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/450289
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/450289?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gang Wang & Yanbin Tang, 2013. "Fractal Dimension of a Random Invariant Set and Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, November.
    2. Gang Wang & Yanbin Tang, 2013. "Fractal Dimension of a Random Invariant Set and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Shuilin Cheng & Yantao Guo & Yanbin Tang, 2014. "Stochastic Nonlinear Thermoelastic System Coupled Sine‐Gordon Equation Driven by Jump Noise," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Shuilin Cheng & Yantao Guo & Yanbin Tang, 2014. "Stochastic Nonlinear Thermoelastic System Coupled Sine-Gordon Equation Driven by Jump Noise," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shuilin Cheng & Yantao Guo & Yanbin Tang, 2014. "Stochastic Nonlinear Thermoelastic System Coupled Sine‐Gordon Equation Driven by Jump Noise," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Da, Nguyen Tien, 2023. "A new result on the fractal dimension estimates of random attractor for non-autonomous random 2D stochastic dynamical type systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:450289. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.