# Blow up of solutions to semilinear non-autonomous wave equations under Robin boundary conditions

## TL;DR

This paper investigates conditions under which solutions to non-autonomous semilinear wave equations with damping, acceleration, and Robin boundary conditions blow up in finite time, including cases with large or negative initial energy.

## Contribution

It provides new sufficient conditions for finite-time blow up of solutions with large or negative initial energy in non-autonomous semilinear wave equations under Robin boundary conditions.

## Key findings

- Finite-time blow up for solutions with large initial energy.
- Blow up results for solutions with negative initial energy.
- Conditions involving damping and accelerating terms leading to blow up.

## Abstract

The problem of blow up of solutions to the initial boundary value problem for non-autonomous semilinear wave equation with damping and accelerating terms under the Robin boundary condition is studied. Sufficient conditions of blow up in a finite time of solutions to semilinear damped wave equations with arbitrary large initial energy are obtained. A result on blow up of solutions with negative initial energy of semilinear second order wave equation with accelerating term is also obtained.