THE MGT-FOURIER MODEL IN THE SUPERCRITICAL CASE

The paper proves exponential stability for the MGT–Fourier system (abstract form (4.1)) when μ = γ − αβ ≥ 0 and η^2 > t(κ) μ, with t(κ) given in (6.2), via a careful energy method using auxiliary Lyapunov-type functionals F, G and the quasi-energy identity (4.4) (Theorem 6.3) . The candidate solution matches the model and characteristic polynomial pη (Section 5) exactly , but its Routh–Hurwitz verification contains a decisive algebraic error: the proposed expression for the third Hurwitz determinant Δ3 lacks the uniform λ^2 factor that must appear from a1 a2 a3 − a1^2 a4 − a3^2 (since a2, a3, a4 each carry λ-factors). This dimensional inconsistency undermines the claimed uniform-in-λ proof of Δ3 > 0 and, hence, the asserted uniform spectral gap. The paper’s result stands correct and complete by energy methods; the model’s Routh–Hurwitz proof is flawed.