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In this paper we consider the semi-linear wave equation: utt − ∆u = ut|ut| in R where 1 < p ≤ 1 + 2 N−1 and p < 3 if N = 1, p 6= 3 if N = 2. We give an energetic criteria and optimal lower bound for blowing up solutions of this equation.

Optimal bounds and blow-up criteria for a semi-linear accretive wave equation