Blow-up for Stochastic Reaction-Diffusion Equations with Jumps

Jianhai Bao () and Chenggui Yuan ()
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Jianhai Bao: Central South University
Chenggui Yuan: Swansea University

Journal of Theoretical Probability, 2016, vol. 29, issue 2, 617-631

Abstract: 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.

Keywords: Stochastic reaction-diffusion equation; Jumps; Wiener random field; Non-negative solution; Blow-up; 60H15; 60G15; 60H05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-014-0589-1

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