The blow-up rate for strongly perturbed semilinear wave equations in the conformal case

TL;DR

This paper investigates the blow-up behavior of strongly perturbed semilinear wave equations with conformal power nonlinearity, providing optimal and auxiliary estimates through Lyapunov functionals and Pohozaev identities.

Contribution

It introduces a novel approach to estimate blow-up rates in perturbed semilinear wave equations using Lyapunov functionals and Pohozaev identities.

Findings

Established an optimal blow-up rate estimate for radial solutions.

Derived two auxiliary estimates with weaker bounds.

Utilized a three-step method involving Lyapunov functionals and Pohozaev identity.

Abstract

We consider in this work some class of strongly perturbed for the semilinear wave equation with conformal power nonlinearity. We obtain an optimal estimate for a radial blow-up solution and we have also obtained two less stronger estimates. These results are achieved in three-steps argument by the construction of a Lyapunov functional in similarity variables and the Pohozaev identity.