Lifespan estimates for 1d damped wave equation with zero moment initial data

TL;DR

This paper provides a precise lifespan estimate for solutions to a one-dimensional semilinear damped wave equation with zero Fourier 0th moment initial data, highlighting a critical change at p=3/2.

Contribution

It offers a sharp lifespan estimate for the damped wave equation under zero moment initial data, revealing a critical behavior at p=3/2.

Findings

Lifespan estimates depend on initial data size.

Behavior changes at p=3/2.

Zero Fourier 0th moment initial data affects lifespan.

Abstract

In this manuscript, a sharp lifespan estimate of solutions to semilinear classical damped wave equation is investigated in one dimensional case when the Fourier 0th moment of sum of initial position and speed is $0$. Especially, it is shown that the behavior of lifespan changes with $p=3/2$ with respect to the size of the initial data.