# Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent

## TL;DR

This paper investigates blow-up phenomena in semilinear wave equations with scale-invariant damping, extending previous results to larger exponents and broader damping constants, especially for super-Fujita exponents.

## Contribution

It extends blow-up results for super-Fujita exponents in damped wave equations to larger exponents and wider damping constants, connecting to the Strauss exponent.

## Key findings

- Blow-up occurs for larger exponents related to the Strauss exponent.
- The blow-up result applies to a wider range of damping constants.
- Extension of previous blow-up results to super-Fujita exponents.

## Abstract

The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case of non-effective damping. In this paper we extend his result in two aspects by showing that: (I) the blow-up will happen for bigger exponent, which is closely related to the Strauss exponent, the critical number for non-damped semilinear wave equations; (II) such a blow-up result is established for a wider range of the constant than the known non-effective one in the damping term.