  We study here the escape time for the fastest diffusing particle from the
boundary of an interval with point-sink killing sources. Killing represents a
degradation that leads to the probabilistic removal of the moving Brownian
particles. We compute asymptotically the mean time it takes for the fastest
particle escaping alive and obtain the extreme statistic distribution. These
computations relies on an explicit expression for the time dependent flux of
the Fokker-Planck equation using the time dependent Green's function and
Duhamel's formula. We obtain a general formula for several point-sink killing,
showing how they directly interact. The range of validity of the present
formula for the mean extreme times of the fastest is evaluated with Brownian
simulations. Finally, we discuss some applications to the early calcium
signaling at neuronal synapses.
