Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions

By Philippe Souplet. Differential and Integral Equations, 2002

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On the generalized Dirichlet problem for viscous Hamilton–Jacobi equations (2004, background): “Almost all these works deals with the equation in the whole space IRN and address questions on the existence, uniqueness and properties of either classical solutions (see for example Amour and Ben-Artzi[1], Ben-Artzi[10, 11], Gilding, Guedda and Kersner[19] and references therein) or solutions in th”
Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena (2004, background): “If, on the contrary, u0 is suitably large, then (II) occurs (see [28]).”
Single-Point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equations in Planar Domains (2010, background): “Global existence and decay for suitably small u0 Ladyzenskaja 56, Filippov 61, Lieberman 86, Alikakos-Bates-Grant 89, Dlotko 91, Alaa 96, Souplet 02, Hesaaraki-Moameni 04, Souplet-Zhang 06, ... Remark: Cauchy problem (Ω = Rn): all solutions global for any p > 0.”