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

Guy Barles (1, 2) , Philippe Laurençot (3) , Christian Stinner (4)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 FDP - Fédération de recherche Denis Poisson
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 Fachbereich Mathematik

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, $p\ge 2$, 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.

Mots clés: convergence to steady state; degenerate parabolic equation; viscosity solutions; gradient source term

Domaines: Equations aux dérivées partielles [math.AP]

Guy Barles, Philippe Laurençot, Christian Stinner. Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton-Jacobi equation. Asymptotic Analysis, 2010, 67 (3-4), pp.229--250. ⟨10.3233/ASY-2010-0981⟩. ⟨hal-00401442⟩