Document Zbl 1329.60215

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Finite time blowup of the stochastic shadow Gierer-Meinhardt system. (English) Zbl 1329.60215

Electron. Commun. Probab. 20, Paper No. 65, 13 p. (2015).

Summary: By choosing some special (random) initial data, we prove that with probability 1, the stochastic shadow Gierer-Meinhardt system blows up pointwisely in finite time.
We also give a (random) upper bound for the blowup time and some estimates about this bound. By increasing the amplitude of the initial data, we can get the blowup in any short time with positive probability.

Cited in 8 Documents

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
60H05	Stochastic integrals
60H30	Applications of stochastic analysis (to PDEs, etc.)
60J65	Brownian motion

Keywords:

stochastic shadow Gierer-Meinhardt system; finite time blowup; Brownian motions; Itô formula

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