On a semilinear wave equation in anti-de Sitter spacetime: the critical case

TL;DR

This paper proves finite-time blow-up of solutions for a semilinear wave equation in anti-de Sitter spacetime in the critical case, using integral representations and iteration methods.

Contribution

It establishes the blow-up phenomenon in the critical case for the wave equation in anti-de Sitter spacetime, combining ODI analysis with explicit integral formulas.

Findings

Finite-time blow-up for solutions in the critical case

Use of explicit integral representation for linear solutions

Combination of ODI and iteration techniques

Abstract

In the present paper we prove the blow-up in finite time for local solutions of a semilinear Cauchy problem associated with a wave equation in anti-de Sitter spacetime in the critical case. According to this purpose, we combine an ODI result with an iteration argument, by using an explicit integral representation formula for the solution to a linear Cauchy problem associated with the wave equation in anti-de Sitter spacetime in one space dimension.