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

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.

26 pages, the title is slightly changed, the introduction is modified, an appendix is added, and the references are updated

References in corpus (1)

• Movement of time-delayed hot spots in Euclidean space

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