Sharp lifespan estimates for Nakao's problem in one space dimension

Abstract

In this paper, we consider Nakao's problem in one space dimension, which couples a semilinear damped wave equation with a semilinear wave equation. For compactly supported energy data satisfying suitable integral sign conditions, we establish sharp lifespan estimates for all powers $p,q>1$. The estimates are classified according to whether the total integral of the initial speed in the wave equation is positive or zero.

This is a new version proving the sharp lifespan estimates for all $p,q>1$