Spreadable distributed systems
type: Item
instance of: scholarly article
title: Spreadable distributed systems
zbMATH Open document ID: 0829.92018
DOI: 10.1016/0895-7177(94)90218-6
published in: Mathematical and Computer Modelling
publication date: 1994-09-22T00:00:00Z
review text: Recently a great number of works have been devoted to the analysis and control of environmental processes where a systematic approach is taken to the modelling. The models are derived from physical laws governing the evolution of the systems. Generally these models are nonlinearly distributed and have to take into account boundary conditions. This is the case of climate models or ecological models describing the evolution of species where the main parameter is a density. However, there exist also empirical models based on experimentation and estimation, namely the gap models which are particularly adapted to forest and grassland dynamics. Our contribution is of theoretical character and is mainly motivated by spreading (or expansion) properties observed for example in desertification, reafforesting or pollution. Mathematically speaking, these phenomena may be expressed by an increasing family \((\omega_t)_t\) of zones where the state is subject to some space constraints. For instance, these zones may be ones where the density is zero, in phenomena of desertification (desert zones) or described by some profile of concentration of pollutants (polluted zones). Obviously, these considerations hold only for distributed systems, since it is necessary to take into account the notion of spatial regions where a certain property exists. Applications may concern various domains of science, particularly control of biophysical and ecological processes. But also, the field is open to pure and applied mathematics.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 92D99
Mathematics Subject Classification ID: 92B05
zbMATH DE Number: 643734
zbMATH Keywords: dynamical distributed systems
zbMATH Keywords: biogeographical processes
zbMATH Keywords: quadratic equations in Hilbert spaces
zbMATH Keywords: increasing family of zones
zbMATH Keywords: spray control
zbMATH Keywords: boundary conditions
zbMATH Keywords: desertification
zbMATH Keywords: reafforesting
zbMATH Keywords: pollution
zbMATH Keywords: space constraints
zbMATH Keywords: distributed systems
author: A. El Jai
author: Khalid Kassara
MaRDI profile type: Publication
full work available at URL: 0895-7177(94)90218-6
OpenAlex ID: W2071180662
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description: scientific article; zbMATH DE number 643734