STABILITY OF A DEGENERATE THERMOELASTIC EQUATION

The paper establishes (i) iR ⊂ ρ(A) by showing A−1 is compact and there are no eigenvalues on the imaginary axis, hence the spectrum on iR is empty, and (ii) a uniform resolvent bound at high frequencies via a contradiction that leverages a weighted Hardy inequality; combined, these yield exponential stability by Gearhart–Prüss, and all steps are justified in the text. In contrast, the model’s argument proves a resolvent contradiction estimate and the key Hardy step, but it never rigorously upgrades “no eigenvalues” on iR to full invertibility (surjectivity) there. It asserts iR ⊂ ρ(A) without supplying the compact-resolvent or an equivalent surjectivity argument that the paper crucially uses. Therefore, the model’s proof is incomplete at this essential step, while the paper’s proof is complete and correct (e.g., compactness of A−1 and the consequent spectral discreteness, Lemma 3.2 and the resolvent sequence argument, and the Gearhart–Prüss invocation) .