Lower and upper bounds for the explosion times of a system of semilinear SPDEs

TL;DR

This paper derives bounds for the explosion times of semilinear stochastic PDE systems, analyzing how noise influences blow-up behavior and extending results to systems driven by two-dimensional Brownian motions.

Contribution

It introduces explicit bounds for blow-up times of semilinear SPDEs using solutions of associated random PDEs and extends the analysis to systems with two-dimensional Brownian noise.

Findings

Bounds for explosion times are established.

Probability estimates for finite-time blow-up are provided.

Impact of noise on solution blow-up is analyzed.

Abstract

In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations. Under suitable assumptions, lower and upper bounds of explosion times are obtained by using explicit solutions of an associated system of random partial differential equations and a formula due to Yor. We also provide an estimate for the probability of the finite-time blow-up. With a suitable choice of parameters, the impact of the noise on the solution is investigated. The above-obtained results are also extended for semilinear SPDEs forced by two dimensional Brownian motions.