Rebuttal to "Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation"

TL;DR

This paper critically examines a 2016 publication on the well-posedness and decay rates of the viscoelastic Kirchhoff equation, identifying major flaws and gaps in its proofs to clarify the validity of its results.

Contribution

It provides a detailed critique of the original proofs, highlighting errors and gaps, thereby clarifying the correctness of the results in the original paper.

Findings

Identifies major flaws in the original proofs.

Highlights gaps in the stability estimates.

Questions the validity of the original results.

Abstract

A paper, entitled "Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation" was published in 2016, in the journal Boletim da Sociedade Paranaense de Matematica. The main results of that paper are stated in Theorem 1.3. Section 2 is devoted to stability estimates for the solutions of the Galerkin approximation (2.1)-(2.2) of (1.2). Section 3 is devoted to the proof of the well-posedness for the Kirchhoff equation (1.2). This rebuttal is written in view to show the major flaws, and gaps in the proofs of this publication.