Single-Point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equations in Planar Domains

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A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up (2016, background): “3), inter alia involving doubly degenerate diffusion, this conclusion seems far from trivial; indeed, various types of gradient-dependent nonlinearities and degeneracies are known to enforce unboundedness of gradients for some solutions even in scalar reaction-diffusion equations [4, 25, 29].”