Sharp lifespan estimates and blow-up rates for the semilinear wave
  equation with time-dependent damping and subcritical nonlinearities

Fujiwara, Kazumasa; Ikeda, Masahiro; Wakasugi, Yuta

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Sharp lifespan estimates and blow-up rates for the semilinear wave equation with time-dependent damping and subcritical nonlinearities

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Author(s): Kazumasa Fujiwara , Masahiro Ikeda , Yuta Wakasugi

Publication date Created: 2016-09-05

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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.