2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124219A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the equilibrium is not stable.v1: 6 pages; v2: 7 pages, fixes a glitch in the main theoremAnalysis of PDEsDynamical Systems37L15 (Primary); 35Q55 (Secondary)text