Finite time blow-up of semi-linear Klein-Gordon equations with positive initial energy in FLRW spacetimes

TL;DR

This paper investigates conditions under which solutions to semi-linear Klein-Gordon equations in FLRW spacetimes blow up in finite time, extending methods from Minkowski spacetime to curved cosmological models.

Contribution

It establishes sufficient conditions for finite-time blow-up of solutions in FLRW spacetimes using the concavity method, adapting techniques from Minkowski spacetime.

Findings

Identifies conditions leading to finite-time blow-up in FLRW spacetimes.

Extends the concavity method to curved spacetime settings.

Provides theoretical criteria for solution blow-up in cosmological models.

Abstract

Blowing-up solutions for semi-linear Klein-Gordon equations are considered in Friedmann-Lema\^itre-Robertson-Walker spacetimes. Some sufficient conditions are shown by applying the concavity method for semi-linear wave equations in the Minkowski spacetime to semi-linear Klein-Gordon equations in FLRW spacetimes.