Blowup of semi-linear equations stochastic partial differential equations sub-solutions and super-solutions
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 22, No 1, (2013), 109p-116p
We obtain upper and lower bounds for the explosion time of a semi-linear heat equation on a bounded $d$-dimensional domain, perturbed by white noise. The bounds we get are expressed in terms of exponential functionals of one-dimensional Brownian motion, whose density function can be explicitly calculated.