| Abstract: |
| In this talk, we study the Cauchy problem for nonlinear Klein-Gordon equations with time dependent damping and mass. Power-type nonlinear terms including derivatives are considered, the equation involves time-dependent coefficients in the scale factor $a(t)$, damping term $b(t)$, and mass term $m(t)$. We establish the occurrence of finite-time blow-up for small initial data and derive upper bounds on the lifespan of blow-up solutions. As a concrete example, we focus on the equations in Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes, which describe the spatial expansion or contraction, and yield some important models of the universe. This talk is based on joint work with Makoto Nakamura, Kimitoshi Tsutaya, and Yuta Wakasugi. |
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