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arXiv · 1609.01035

Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity

Kazumasa Fujiwara·Masahiro Ikeda·Yuta Wakasugi
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Abstract

We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan estimates of solutions. Upper estimates are proved by an ODE argument, and lower estimates are given by a method of scaling variables.

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Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi. 2016-11-20. Estimates of lifespan and blow-up rates for the wave equation with a time-dependent damping and a power-type nonlinearity. https://doi.org/10.1619/fesi.62.157

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