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arXiv · 0704.3989

Instability of an equilibrium of a partial differential equation

Michael Robinson
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Abstract

A 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.

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Michael Robinson. 2007-09-09. Instability of an equilibrium of a partial differential equation. https://arxiv.org/abs/0704.3989

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