IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v296y2023i6p2352-2365.html
   My bibliography  Save this article

A characterization of well‐posedness for the second order abstract Cauchy problems with finite delay

Author

Listed:
  • Seyedeh Marzieh Ghavidel

Abstract

In this work, we introduce a strongly continuous one‐parameter family of bounded linear operators that completely describes the well‐posedness of a second order abstract differential delay equation in the initial history space Lp([−r,0];X)$L^p([-r,0];X)$, r>0$r>0$. This family, which satisfies a specific functional equation is applied to characterize the mild solution of the considered second order delay equation.

Suggested Citation

  • Seyedeh Marzieh Ghavidel, 2023. "A characterization of well‐posedness for the second order abstract Cauchy problems with finite delay," Mathematische Nachrichten, Wiley Blackwell, vol. 296(6), pages 2352-2365, June.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:6:p:2352-2365
    DOI: 10.1002/mana.202000517
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202000517
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202000517?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. Kai Liu, 2012. "On Regularity Property of Retarded Ornstein–Uhlenbeck Processes in Hilbert Spaces," Journal of Theoretical Probability, Springer, vol. 25(2), pages 565-593, June.
    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.

      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:296:y:2023:i:6:p:2352-2365. 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: 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.