Spreadable distributed systems
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.
scientific article; zbMATH DE number 643734
scientific article