Abstract
<p style='text-indent:20px;'>In the present paper, we study small data blow-up of the semi-linear wave equation with a scattering dissipation term and a time-dependent mass term from the aspect of wave-like behavior. The Strauss type critical exponent is determined and blow-up results are obtained to both sub-critical and critical cases with corresponding upper bound lifespan estimates. For the sub-critical case, our argument does not rely on the sign condition of dissipation and mass, which gives the extension of the result in [<xref ref-type="bibr" rid="b14">14</xref>]. Moreover, we show the blow-up result for the critical case which is a new result.</p>
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