Affiliations: Laboratoire de Mathématiques et Physique Théorique, CNRS UMR 6083, Fédération Denis Poisson, Université François Rabelais, Parc de Grandmont, F-37200 Tours, France. E-mail: [email protected] | Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, F-31062 Toulouse Cedex 9, France. E-mail: [email protected] | Fachbereich Mathematik, Universität Duisburg-Essen, D-45117 Essen, Germany. E-mail: [email protected]
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.
Keywords: convergence to steady state, degenerate parabolic equation, viscosity solutions, gradient source term
