Decay Estimates for a Viscous Hamilton-Jacobi Equation with Homogenious   Dirichet Boundary Conditions
  Global classical solutions to the viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions are shown to converge to zero at the same speed as the linear heat semigroup when p > 1. For p = 1, an exponential decay to zero is also obtained in one space dimension but the rate depends on a and differs from that of the linear heat equation. Finally, if 0 < p < 1 and a < 0, finite time extinction occurs for non-negative solutions. 
Said Benachour (IECN), Simona Dabuleanu-Hapca (SIMBIOS), Philippe   Lauren\c{c}ot (MIP)