We consider the viscous Hamilton-Jacobi (VHJ) equation ut-Δ u=|∇ u| p+ h (x). For the
Dirichlet problem with p> 2, it is known that gradient blow-up may occur in finite time (on the …

Abstract Consider the diffusive Hamilton-Jacobi equation ut= Δ u+|∇ u| p, p> 2, on a
bounded domain Ω with zero-Dirichlet boundary conditions, which arises in the KPZ model …

This paper is devoted to analyse a case of singularity formation in infinite time for a
semilinear heat equation involving linear diffusion and superlinear convection. A feature to …

We consider the diffusive Hamilton–Jacobi equation, with superquadratic Hamiltonian,
homogeneous Dirichlet conditions and regular initial data. It is known from [4](Barles–DaLio …

We study the existence of solutions of a nonlinear parabolic problem of Cauchy–
Dirichlettype having a lower order term which depends on the gradient. The model we have …

Global classical solutions to the viscous Hamilton–Jacobi equation ut− Δu= a|∇ u| p in
(0,∞)× Ω with homogeneous Dirichlet boundary conditions are shown to converge to zero in …

We extend some previous existence results for quenching type parabolic problems involving
a negative power of the unknown in the equation to the case of merely integrable initial data …

We investigate the diffusive Hamilton–Jacobi equation ut− u=|∇ u| p with p> 1, in a smooth
bounded domain of Rn with homogeneous Neumann boundary conditions and W1,∞ initial …

We study the nonnegative solutions of the viscous Hamilton–Jacobi problem {ut− ν Δ u+|∇
u| q= 0, u (0)= u 0, in Q Ω, T= Ω×(0, T), where q> 1, ν≧ 0, T∈(0,∞], and Ω= RN or Ω is a …

We investigate the convergence to steady states of the solutions to the one-dimensional
viscous Hamilton–Jacobi equation∂ tu−∂ x 2 u=|∂ xu| p, where (t, x)∈(0,∞)×(− 1, 1) and …