Post–operative glioblastoma cancer cell distribution in the peritumoural oedema

The paper formulates the MRI-fitting minimization problem over a spread parameter ξ and states Hypothesis H about how initial spread in oedema relates to later invasion, but it does not provide rigorous proofs of existence of a minimizer or of H; both are posed and explored numerically and left “under analytical investigation” . The candidate (model) solution correctly observes continuity-based strategies (Weierstrass on a compact ξ-interval) and offers a general counterexample to H via bistable dynamics, plus sufficient conditions for H under KPP-type, order-preserving flows. However, part of its coercivity-at-infinity argument is misaligned with the paper’s specific logistic-type, bounded-growth macro-PDE, which can uniformly bound solutions and therefore may defeat the proposed blow-up at ξ→∞; moreover, the model’s monotonicity claims rely on order-preserving semigroup assumptions unlikely to hold for the paper’s full anisotropic diffusion–adhesion–micro/macro moving-boundary system . Hence, both the paper and the model solution leave gaps: the paper in not proving the posed statements, and the model in invoking extra assumptions not established for the paper’s system.