Blow-up rate for a semi-linear accretive wave equation

TL;DR

This paper investigates the blow-up rate of solutions to a semi-linear wave equation with an accretive nonlinearity, establishing the behavior of solutions that have bounded below energy.

Contribution

The paper introduces an energy framework for the semi-linear wave equation and determines the blow-up rate for solutions with bounded below energy, advancing understanding of blow-up dynamics.

Findings

Established an energy associated with the semi-linear wave equation.

Derived the blow-up rate for solutions with bounded below energy.

Provided insights into the blow-up behavior in the context of accretive nonlinearities.

Abstract

In this paper we consider the semi-linear wave equation: $u_{tt}-\Delta u=u_t|u_t|^{p-1}$ in $\mathbb{R}^N$. We provide an associated energy. With this energy we give the blow-up rate for blowing up solutions in the case of bounded below energy.