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In this paper we study blow-up and lifespan estimate for solutions to theCauchy problem with small data for semilinear wave equations with scatteringdamping and negative mass term. We show that the negative mass term will play adominant role when the decay of its coefficients is not so fast, thus thesolutions will blow up in a finite time. What is more, we establish a lifespanestimate from above which is much shorter than the usual one.

Short time blow-up by negative mass term for semilinear wave equations with small data and scattering damping