Quenching time and probability estimates for a stochastic reaction-diffusion system with coupled inner singular absorption terms driven by mixed noises

Abstract: This paper investigates a stochastic parabolic system under Robin boundary conditions, for which the deterministic counterpart exhibits finite quenching. The stochastic system incorporates mixed noise, combining standard one-dimensional Brownian motion and fractional Brownian motion. Under appropriate assumptions, we derive explicit lower and upper bounds for the quenching time of the solution and establish the global existence of a weak solution. Leveraging Malliavin calculus, we further obtain a quantifiable lower and upper bound on the quenching probability. To complement the theoretical analysis, we design a numerical scheme tailored to the system and present results that validate the analytical predictions, offering insights into the interplay between noise and quenching behaviour.