This work is concerned with the proof of Lp-Lq decay estimates for solutions of the Cauchy problem for utt-λ2（t）b2（t） △ u =0. The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. The authors’ main interest is devoted to the critical case where one has an interesting interplay between the growing and the oscillating part.
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