The Profile of Boundary Gradient Blowup for the Diffusive Hamilton–Jacobi Equation

DOI10.1093/IMRN/RNW154zbMath1405.35097arXiv1508.06766OpenAlexW2963195673MaRDI QIDQ4612023

Philippe Souplet, Alessio Porretta

Publication date: 22 January 2019

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.06766

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Quasilinear parabolic equations (35K59)

Related Items (16)

Remarks on the generalized Cauchy-Dirichlet problem for graph mean curvature flow with driving force ⋮ Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms ⋮ Analysis of the attainment of boundary conditions for a nonlocal diffusive Hamilton-Jacobi equation ⋮ Continuation beyond interior gradient blow-up in a semilinear parabolic equation ⋮ Lipschitz regularity for viscous Hamilton-Jacobi equations with \(L^p\) terms ⋮ Properties of solutions to porous medium problems with different sources and boundary conditions ⋮ Singularity formation and regularization at multiple times in the viscous Hamilton–Jacobi equation ⋮ Asymptotic behavior of global solutions to a class of heat equations with gradient nonlinearity ⋮ Gradient blow-up rates and sharp gradient estimates for diffusive Hamilton-Jacobi equations ⋮ Gradient blowup behavior for a viscous Hamilton-Jacobi equation with degenerate gradient nonlinearity ⋮ Single-point gradient blow-up on the boundary for diffusive Hamilton-Jacobi equation in domains with non-constant curvature ⋮ Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation ⋮ Unnamed Item ⋮ A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton–Jacobi equations ⋮ Singular Neumann Boundary Problems for a Class of Fully Nonlinear Parabolic Equations in One Dimension ⋮ Complete classification of gradient blow-up and recovery of boundary condition for the viscous Hamilton-Jacobi equation

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