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Abstract
In this paper, we obtain lower and upper bounds for the blow-up times for a system of semilinear stochastic partial differential equations. Under suitable assumptions, lower and upper bounds of the explosive times are obtained by using explicit solutions of an associated system of random partial differential equations and a formula due to Yor. We provide lower and upper bounds for the probability of finite-time blow-up solution as well. The above obtained results are also extended for semilinear SPDEs forced by two-dimensional Brownian motions.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability
Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
Additional information
Funding
The First author is supported by the University Research Fellowship of Periyar University, India. M. T. Mohan would like to thank the Department of Science and Technology (DST), India for Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (IFA17-MA110). The Third author is supported by the Fund for Improvement of Science and Technology Infrastructure (FIST) of the Department of Science and Technology (SR/FST/MSI-115/2016). The authors sincerely would like to thank the reviewers for their valuable comments and suggestions, which helped us to improve the manuscript significantly.