Instability of an equilibrium of a partial differential equation

Details Instability of an equilibrium of a partial differential equation Instability of an equilibrium of a partial differential equation

2007-04-30

arxiv.org/abs/0704.3989v2

Mathematics

Analysis of PDEs

12 pages

Scientific paper

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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