2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137488A nonlinear parabolic differential equation with a quadratic nonlinearity is presented which has at least one equilibrium. The linearization about this equilibrium is asymptotically stable, but by using a technique inspired by H. Fujita, we show that the equilibrium is unstable in the nonlinear setting. The perturbations used have the property that they are small in every $L^p$ norm, yet they result in solutions which fail to be global.12 pagesAnalysis of PDEsDynamical Systems37L15 (Primary) 35Q55 (Secondary)text