Instability of an equilibrium with negative definite linearization

Details Instability of an equilibrium with negative definite linearization Instability of an equilibrium with negative definite linearization

2007-02-19

arxiv.org/abs/math/0702560v2

Mathematics

Analysis of PDEs

v1: 6 pages; v2: 7 pages, fixes a glitch in the main theorem

Scientific paper

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.

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