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Blow-up for Stochastic Reaction-Diffusion Equations with Jumps

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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.

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Acknowledgments

The authors are greatly indebted to the referees, whose very careful comments and helpful suggestions on the earlier version of the paper greatly improved the quality of the paper. The research is supported in part by NSFC (No. 11401592).

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Authors and Affiliations

  1. Department of Mathematics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Jianhai Bao

  2. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK

    Chenggui Yuan

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  1. Jianhai Bao
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  2. Chenggui Yuan
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Correspondence to Chenggui Yuan.

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Bao, J., Yuan, C. Blow-up for Stochastic Reaction-Diffusion Equations with Jumps. J Theor Probab 29, 617–631 (2016). https://doi.org/10.1007/s10959-014-0589-1

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  • DOI: https://doi.org/10.1007/s10959-014-0589-1

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