Survival probability of a diffusing particle constrained by two moving, absorbing boundaries

We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located located at the point x in (-L,L), in the presence of two moving absorbing boundaries located at \pm(L+ct). The result is Q(y,\lambda) = \sum_{n=-\infty}^\infty (-1)^n \cosh(ny) \exp(-n^2\lambda), where y=cx/D, \lambda = cL/D and D is the diffusion constant of the particle. The results may be extended to the case where the absorbing boundaries have different speeds. As an application, we compute the asymptotic survival probability for the trapping reaction A + B -> B, for evanescent traps with a long decay time.