Blow-up estimates for a system of semilinear SPDEs with fractional noise

S. Sankar, Manil T. Mohan, S. Karthikeyan

Published 2022-07-25Version 1

In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations driven by two-dimensional fractional Brownian motion. Under suitable assumptions, lower and upper bounds for the blow-up time of the solution are obtained by using explicit solutions of an associated system of random partial differential equations and formula due to Yor. We also provide an estimate for the finite-time blow-up solutions of a system by choosing suitable parameters. Further, a lower bound for the blow-up probability of solutions is provided by using Malliavin calculus.