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Finite-time blowup and existence of global positive solutions of a semi-linear SPDE

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  • Dozzi, Marco
  • López-Mimbela, José Alfredo

Abstract

We consider stochastic equations of the prototype on a smooth domain , with Dirichlet boundary condition, where [beta], [kappa] are positive constants and {Wt,t>=0} is a one-dimensional standard Wiener process. We estimate the probability of finite-time blowup of positive solutions, as well as the probability of existence of non-trivial positive global solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:6:p:767-776
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    References listed on IDEAS

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    1. Bergé, Benjamin & D. Chueshov, Igor & Vuillermot, Pierre-A., 2001. "On the behavior of solutions to certain parabolic SPDE's driven by wiener processes," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 237-263, April.
    2. Gyöngy, István & Rovira, Carles, 2000. "On Lp-solutions of semilinear stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 90(1), pages 83-108, November.
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    Cited by:

    1. 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.
    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. 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.
    5. Tian, Rongrong & Wei, Jinlong & Wu, Jiang-Lun, 2021. "On a generalized population dynamics equation with environmental noise," Statistics & Probability Letters, Elsevier, vol. 168(C).

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