info:eu-repo/semantics/report
Lower and Upper Bounds of the Explosion Time of a Reaction-Diffusion System Perturbed by Brownian Motion
Autor
JOSE ALFREDO LOPEZ MIMBELA
Institución
Resumen
We investigate lower and upper bounds for the blow-up time of a system
of semilinear stochastic partial differential equations (SPDEs). From these
bounds we obtain lower and upper bounds for the probability of explosion in
finite time of the system. The lower bound is obtained from a related system
of random partial differential equations, and is given in terms of the Laplace
transform of a perpetual integral functional of a standard Brownian motion.
The upper bound is given in terms of the expected value of a similar perpetual
integral functional. We also extend the approach introduced by Chow (2011)
to our system of SPDEs, and get an explosion result in Lp-norm, for any
1< p < Infinito.
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