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Explosive solutions of parabolic stochastic partial differential equations with lévy noise

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  • In this paper, we study the explosive solutions to a class of parbolic stochastic semilinear differential equations driven by a Lévy type noise. The sufficient conditions are presented to guarantee the existence of a unique positive solution of the stochastic partial differential equation under investigation. Moreover, we show that positive solutions will blow up in finite time in mean Lp-norm sense, provided that the initial data, the nonlinear term and the multiplicative noise satisfies some conditions. Several examples are presented to illustrate the theory. Finally, we establish a global existence theorem based on a Lyapunov functional and prove that a stochastic Allen-Cahn equation driven by Lévy noise has a global solution.

    Mathematics Subject Classification: Primary: 60H15, 60J75.


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