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The survival probabilities of a ``prisoner'' diffusing in an expanding cageand a ``daredevil'' diffusing at the edge of a receding cliff are investigated.When the diffuser reaches the boundary, he dies. For ``marginal'' boundarymotion, i.e., the cage length grows as $\sqrt{At}$ or the cliff locationrecedes as $x_0(t)=-\sqrt{At}$ and the daredevil diffuses within the domain$x>x_0$, the survival probability of the diffuser exhibits non-universalpower-law behavior, $S(t)\sim t^{-\b}$, which depends on the relative rates ofboundary and diffuser motion. Heuristic approaches are applied for the cases of``slow'' and ``fast'' boundary motion which yield approximate expressions for$\b$. An asymptotically exact analysis of these two problems is also performedand the approximate expressions for $\b$ coincide with the exact results fornearly entire range of possible boundary motions.Comment: 11 pages, plain TeX, 1 figure (not included), submitted to J. Stat.  Phy

Life and death in an expanding cage and at the edge of a receding cliff