An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains

The paper’s core existence relation χ(µ) = sqrt(2/D_L)·ℓ and its consequences are consistent and repeatedly stated (e.g., eqs. (2.31), (3.20), (4.31)), leading to thresholds D_L = 2/(K^2 χ(µ)^2) and, equivalently, L = (√D·K/√2)·χ(µ). The candidate solution inverts this, asserting K^2 D_L/2 = χ(µ)^2 and using D_L < 2[χ(µ)]^2/K^2, which contradicts the paper and flips the dependence on χ. The candidate also assumes the outer field is decreasing, whereas the paper proves monotone increase in the relevant regimes. By contrast, the candidate’s model-specific conclusions (the Schnakenberg separating curve a_c(b), the Brusselator f_c ≈ 0.769, and the GM ‘no replication’ result) match the paper. Therefore, the paper is correct and complete on these points; the model’s outline errs in the key χ–D_L relation and in monotonicity.