Pattern formation in a cell migration model with aggregation and diffusion

The paper’s Theorem 4.4 claims that for any T>0 and any u0 in C^{1,β}[0,1], the Dirichlet problem for u_t = (D(u) u_x)_x under the sign-changing diffusion condition (2.7) has no weak solution. But the trivial solution u ≡ 0 is a weak solution in the sense of Definition 4.1, satisfies the Dirichlet boundary condition, and corresponds to the admissible initial datum u0 ≡ 0 ∈ C^{1,β}[0,1], contradicting the universal nonexistence claim. This directly refutes Theorem 4.4 as stated (Theorem and proof excerpt: ; weak solution definition: ; PDE and diffusion-condition setup: ; Dirichlet boundary setting elsewhere in Section 4: ). The proof also misapplies Theorem 4.1 (Neumann, forward-region existence) after time reversal and asserts a contradiction from increased regularity, which is not logically valid (, ).