IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v297y2024i12p4535-4581.html
   My bibliography  Save this article

Visco‐elastic damped wave models with time‐dependent coefficient

Author

Listed:
  • Halit Sevki Aslan
  • Michael Reissig

Abstract

In this paper, we study the following Cauchy problem for linear visco‐elastic damped wave models with a general time‐dependent coefficient g=g(t)$g=g(t)$: ★ utt−Δu−g(t)Δut=0,(t,x)∈(0,∞)×Rn,u(0,x)=u0(x),ut(0,x)=u1(x),x∈Rn.$$\begin{equation} {\begin{cases} u_{tt}- \Delta u {- g(t)\Delta u_t}=0, &(t,x) \in (0,\infty) \times \mathbb {R}^n,\\ u(0,x)= u_0(x),\quad u_t(0,x)= u_1(x), & x \in \mathbb {R}^n. \end{cases}} \end{equation}$$We are interested to study the influence of the damping term −g(t)Δut$-g(t)\Delta u_t$ on qualitative properties of solutions to (★) as decay estimates for energies of higher order and the parabolic effect. The main tools are related to WKB‐analysis. We apply elliptic as well as hyperbolic WKB‐analysis in different parts of the extended phase space.

Suggested Citation

  • Halit Sevki Aslan & Michael Reissig, 2024. "Visco‐elastic damped wave models with time‐dependent coefficient," Mathematische Nachrichten, Wiley Blackwell, vol. 297(12), pages 4535-4581, December.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:12:p:4535-4581
    DOI: 10.1002/mana.202300341
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202300341
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202300341?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
    ---><---

    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:bla:mathna:v:297:y:2024:i:12:p:4535-4581. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.