Resumen de Convergence to steady states for a one-dimensional viscous Hamilton¿Jacobi equation with Dirichlet boundary conditions

Philippe Laurençot

• We investigate the convergence to steady states of the solutions to the one-dimensional viscous Hamilton¿Jacobi equation ?tu - ?x2u = |?xu|p, where (t,x) in (0,8) × (-1,1) and p in (0,1), with homogeneous Dirichlet boundary conditions. For that purpose, a Liapunov functional is constructed by the approach of Zelenyak (1968). Instantaneous extinction of ?xu on a subinterval of (-1,1) is shown for suitable initial data.