## Electronic Communications in Probability

### Finite time blowup of the stochastic shadow Gierer-Meinhardt System

#### Abstract

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.

#### Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 65, 13 pp.

Dates
Accepted: 23 September 2015
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465320992

Digital Object Identifier
doi:10.1214/ECP.v20-4298

Mathematical Reviews number (MathSciNet)
MR3407209

Zentralblatt MATH identifier
1329.60215

Rights

#### Citation

Li, Fang; Xu, Lihu. Finite time blowup of the stochastic shadow Gierer-Meinhardt System. Electron. Commun. Probab. 20 (2015), paper no. 65, 13 pp. doi:10.1214/ECP.v20-4298. https://projecteuclid.org/euclid.ecp/1465320992

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