Sharp lifespan estimates of blowup solutions to semilinear wave equations with time-dependent effective damping

Abstract

We consider the initial value problem for the semilinear wave equation with time-dependent effective damping. The interest is the behavior of lifespan of solutions in view of the asymptotic profile of the damping as $t\to \infty$. The result of this paper is the sharp lifespan estimates of blowup solutions for general time-dependent damping including threshold cases between effective and overdamping.

arXiv comment20 pages, typos are corrected, references are updated, to appear in J. Hyperbolic Differ. Equ

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• Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetime
• Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution