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Instability of an equilibrium with negative definite linearization

Michael Robinson
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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.

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Michael Robinson. 2007-02-20. Instability of an equilibrium with negative definite linearization. https://arxiv.org/abs/math/0702560

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