Instability of an equilibrium of a partial differential equation

2007/04/30 by Michael Robinson, Robinson, Michael · 2 citations
Computer Science · Engineering · Mathematics · #37L15 (Primary) 35Q55 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP #math.DS #msc:35Q55 #msc:37L15

paper · pdf · doi:10.48550/arxiv.0704.3989

12 pages

openalex publication_date 2007/04/30 · arxiv created 2007/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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