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This article introduces a novel "bootstrap domain-of-dependence" concept,according to which, for all time following a given illumination period ofarbitrary duration, the wave field scattered by an obstacle is encoded in thehistory of boundary scattering events for a time-length equal to the diameterof the obstacle, measured in time units. Resulting solution bounds provideestimates on the solution values in terms of a short-time history record, andthey establish super-algebraically fast decay (i.e., decay faster than anynegative power of time) for a wide range of scattering obstacle--includingcertain types of "trapping" obstacles whose periodic trapped orbits span a setof positive volumetric measure, and for which no previous fast-decay theory wasavailable. The results, which do not rely on consideration of the Lax-Phillipscomplex-variables scattering framework and associated resonance-free regions inthe complex plane, utilize only real-valued frequencies, and follow from use ofGreen functions and boundary integral equation representations in the frequencyand time domains, together with a certain $q$-growth condition on thefrequency-domain operator resolvent.

"Bootstrap Domain of Dependence": Bounds and Time Decay of Solutions of the Wave Equation