Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton–Jacobi equation

Abstract

Convergence to a single steady state is shown for non-negative and radially symmetric solutions to a diffusive Hamilton–Jacobi equation with homogeneous Dirichlet boundary conditions, the diffusion being the p-Laplacian operator, p≥2, and the source term a power of the norm of the gradient of u. As a first step, the radially symmetric and non-increasing stationary solutions are characterized.