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We study the trajectorywise blowup behavior of a semilinear partialdifferential equation that is driven by a mixture of multiplicative Brownianand fractional Brownian motion, modeling different types of randomperturbations. The linear operator is supposed to have an eigenfunction ofconstant sign, and we show its influence, as well as the influence of itseigenvalue and of the other parameters of the equation, on the occurrence of ablowup in finite time of the solution. We give estimates for the probability offinite time blowup and of blowup before a given fixed time. Essential tools arethe mild and weak form of an associated random partial differential equation.

Large time behavior of semilinear stochastic partial differential equations perturbed by a mixture of Brownian and fractional Brownian motions