Instability of an equilibrium with negative definite linearization
arXiv:math/0702560
Abstract
A 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 theorem