Global existence and blow-up for semilinear damped wave equations in three space dimensions

TL;DR

This paper proves the global existence of solutions for semilinear damped wave equations in three dimensions with small initial data, and establishes the sharp lifespan, confirming Takamura's conjecture.

Contribution

It extends previous results by removing the spherical symmetry assumption and provides the precise lifespan of solutions, confirming a conjecture in the field.

Findings

Proved small data global existence without symmetry assumptions.

Established the sharp lifespan of solutions.

Confirmed Takamura's conjecture on solution lifespan.

Abstract

We consider initial value problem for semilinear damped wave equations in three space dimensions. We show the small data global existence for the problem without the spherically symmetric assumption and obtain the sharp lifespan of the solutions. This paper is devoted to a proof of the Takamura's conjecture on the lifespan of solutions.