A remark on the critical exponent for the semilinear damped wave equation on the half-space

TL;DR

This paper establishes the critical exponent for the semilinear damped wave equation on the half-space by proving the non-existence of global solutions, thus advancing understanding of solution behavior in this setting.

Contribution

It determines the critical exponent for the semilinear damped wave equation on the half-space, which was previously unknown.

Findings

Non-existence of global solutions for certain exponents

Identification of the critical exponent in any space dimension

Extension of known results to the half-space setting

Abstract

In this short notice, we prove the non-existence of global solutions to the semilinear damped wave equation on the half-space, and we determine the critical exponent for any space dimension.