Instability of an equilibrium with negative definite linearization
Analysis of PDEs
2007-05-23 v2 Dynamical Systems
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.
Cite
@article{arxiv.math/0702560,
title = {Instability of an equilibrium with negative definite linearization},
author = {Michael Robinson},
journal= {arXiv preprint arXiv:math/0702560},
year = {2007}
}
Comments
v1: 6 pages; v2: 7 pages, fixes a glitch in the main theorem