IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i9p5605-5635.html
   My bibliography  Save this article

Finite-time blow-up of a non-local stochastic parabolic problem

Author

Listed:
  • Kavallaris, Nikos I.
  • Yan, Yubin

Abstract

The main aim of the current work is the study of the conditions under which (finite-time) blow-up of a non-local stochastic parabolic problem occurs. We first establish the existence and uniqueness of the local-in-time weak solution for such problem. The first part of the manuscript deals with the investigation of the conditions which guarantee the occurrence of noise-induced blow-up. In the second part we first prove the C1-spatial regularity of the solution. Then, based on this regularity result, and using a strong positivity result we derive, for first in the literature of SPDEs, a Hopf’s type boundary value point lemma. The preceding results together with Kaplan’s eigenfunction method are then employed to provide a (non-local) drift term induced blow-up result. In the last part of the paper, we present a method which provides an upper bound of the probability of (non-local) drift term induced blow-up.

Suggested Citation

  • Kavallaris, Nikos I. & Yan, Yubin, 2020. "Finite-time blow-up of a non-local stochastic parabolic problem," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5605-5635.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5605-5635
    DOI: 10.1016/j.spa.2020.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414920302052
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2020.04.002?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dozzi, Marco & López-Mimbela, José Alfredo, 2010. "Finite-time blowup and existence of global positive solutions of a semi-linear SPDE," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 767-776, 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.
    1. Lv, Guangying & Wei, Jinlong, 2020. "Blowup solutions for stochastic parabolic equations," Statistics & Probability Letters, Elsevier, vol. 166(C).
    2. Dung, Nguyen Tien, 2019. "The probability of finite-time blowup of a semi-linear SPDE with fractional noise," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 86-92.
    3. Muhammad Shoaib Arif & Kamaleldin Abodayeh & Yasir Nawaz, 2023. "A Computational Scheme for Stochastic Non-Newtonian Mixed Convection Nanofluid Flow over Oscillatory Sheet," Energies, MDPI, vol. 16(5), pages 1-17, February.
    4. Tian, Rongrong & Wei, Jinlong & Wu, Jiang-Lun, 2021. "On a generalized population dynamics equation with environmental noise," Statistics & Probability Letters, Elsevier, vol. 168(C).

    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:eee:spapps:v:130:y:2020:i:9:p:5605-5635. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.