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Blow-up solution to an abstract non-local stochastic heat equation with Lévy noise

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  • Liang, Fei
  • Zhang, Yidi
  • Zhao, Shuangshuang

Abstract

This paper investigates explosive solutions to a class of non-local stochastic heat equations driven by Lévy noise. We establish sufficient conditions to show that the positive solution will blow-up in finite time.

Suggested Citation

  • Liang, Fei & Zhang, Yidi & Zhao, Shuangshuang, 2024. "Blow-up solution to an abstract non-local stochastic heat equation with Lévy noise," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223002006
    DOI: 10.1016/j.spl.2023.109976
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    References listed on IDEAS

    as
    1. Mueller, Carl, 1998. "The heat equation with Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 67-82, May.
    2. 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.
    3. Lv, Guangying & Wei, Jinlong, 2020. "Blowup solutions for stochastic parabolic equations," Statistics & Probability Letters, Elsevier, vol. 166(C).
    4. Z. Dong, 2008. "On the Uniqueness of Invariant Measure of the Burgers Equation Driven by Lévy Processes," Journal of Theoretical Probability, Springer, vol. 21(2), pages 322-335, June.
    Full references (including those not matched with items on IDEAS)

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