Blow-up estimates for a system of semilinear SPDEs driven by mixed fractional Brownian motions

2022/07/25 by Sankar, S., Mohan, Manil T., Karthikeyan, S.
#35B44 #35R60 #60G22 #60H07 #60H15 #74H35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2207.12343

Abstract

In this paper, we obtain the existence and finite-time blow-up for the solution to a system of semilinear stochastic partial differential equations driven by a combination of Brownian and fractional Brownian motions. Under suitable assumptions, lower and upper bounds for the finite-time blow-up solution are obtained. We provide sufficient conditions for the existence of a global weak solution to the system. Further, a lower bound for the probability of the finite-time blow-up solution of the considered system is provided by using Malliavin calculus.

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