2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116485Global 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.20 pagesAnalysis of PDEs35B40, 35K55, 35K60, 35B33, 35B35text