The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions

TL;DR

This paper proves a conjecture regarding the minimum lifespan of solutions to semilinear wave equations in two dimensions, considering different initial conditions, and establishes sharp lower bounds.

Contribution

It provides the first rigorous proof of Takamura's conjecture on lifespan bounds for semilinear wave equations in 2D, distinguishing cases based on initial data.

Findings

Established sharp lower bounds for solution lifespan

Validated Takamura's conjecture in two-dimensional cases

Differentiated lifespan bounds based on initial speed integral

Abstract

This paper is devoted to a proof of the conjecture in Takamura(2015) on the lower bound of the lifespan of solutions to semilinear wave equations in two space dimensions. The result is divided into two cases according to the total integral of the initial speed.