A Classification of Spikes and Plateaus

摘要: In this paper we classify local maxima into spikes and plateaus. We give analytic definitions for plateaus in terms of a nonlocal gradient fourth order derivative. higher dimensions the Hesse matrix $\Delta f(x)$ is relevance. This classification applied to pattern formation models mathematical physics biology, including Cahn-Hilliard equations, chemotaxis reaction-diffusion Gierer-Meinhardt models, Gray-Scott models. show some these examples that stability spatial patterns depends on spike versus plateau type solution. prove, example, scalar equations any dimension cannot have stable steady states.