On Nonlinear Differential Equations That Describe Localized Processes

Abstract

In this paper we want to characterize nonlinear differential equations that describe processes allowing a localization operation in each subdomain of domain in which we consider the process. We formulate this localization condition by means of visual representations and give this operation a mathematical sense. Then we obtain a general form for such equation as well as put in it certain general physical contents, taking into account the fact that nonlinear operators from physically intelligent equations satisfy this condition.