Shock-fronted travelling waves in a reaction-diffusion model with nonlinear forward-backward diffusion

The paper correctly derives the slow–fast reductions for both regularisations, identifies the layer problems and shock endpoints, and uses the matching condition Δp(c)=0 to select the speed; however, it explicitly omits key persistence arguments (transversality, Melnikov analysis) and, for the viscous case, the necessary treatment of loss of normal hyperbolicity at folds, deferring to the literature without proof. The candidate solution reproduces the same reduced and layer problems (including the equal-F/‘equal-W’ rule) and outlines a Fenichel–exchange argument, but it: (i) glosses over the fold issue in the viscous case where standard Fenichel theory does not apply; (ii) contains a slip in the non-local first-order reformulation (missing a v^2 term); and (iii) asserts a sign-change for Δp(c) without proof. Therefore, both are incomplete: the paper by omission, the model by unaddressed technical gaps and a minor algebraic error. Key points of agreement (reduced flow, layer endpoints, Δp matching, p approximately constant across the layer) are consistent with the paper’s derivations and figures.