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Blow-up for Stochastic Reaction-Diffusion Equations with Jumps

Author

Listed:
  • Jianhai Bao

    (Central South University)

  • Chenggui Yuan

    (Swansea University)

Abstract

In this paper, we focus on stochastic reaction-diffusion equations with jumps. By a new auxiliary function, we investigate non-negative property of the local strong (variational) solutions, which applies to stochastic reaction-diffusion equations with highly nonlinear noise terms. As a byproduct, we study the problem of non-existence of global strong solutions by imposing appropriate conditions on the drift terms, which can cover many more models than the existing literature. Moreover, we also investigate the subject of Lévy-type noise-induced explosion by bringing some plausible assumptions to bear on the noise terms, which, however, need not guarantee local strong (variational) solutions to enjoy the non-negative property. Meanwhile, several examples are presented to illustrate the theory established.

Suggested Citation

  • Jianhai Bao & Chenggui Yuan, 2016. "Blow-up for Stochastic Reaction-Diffusion Equations with Jumps," Journal of Theoretical Probability, Springer, vol. 29(2), pages 617-631, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0589-1
    DOI: 10.1007/s10959-014-0589-1
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    References listed on IDEAS

    as
    1. Chow, Pao-Liu & Khasminskii, Rafail, 2014. "Almost sure explosion of solutions to stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 639-645.
    2. Chow, Pao-Liu & Liu, Kai, 2012. "Positivity and explosion in mean Lp-norm of stochastic functional parabolic equations of retarded type," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1709-1729.
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