Page 125 -

7 Reaction-Diffusion Equations – Homogeneous and Heterogeneous Environments
119

independent of the position variable x) is by now a classical subject, the study
of theinteractionof thespatial structurewithreactionand diffusionhas only
started recently, particularly in biological/environmental/population dynamics
models. In this respect we cite [10]:

In the last two decades, it has become increasingly clear that the spatial
dimension and, in particular, the interplay between environmental het-
erogeneity and individual movement, is an extremely important aspect
of ecological dynamics.

In many cases when persistence of species or invasion of species into environ-
mentsareanalyzed,thestandardassumptionofhomogeneityoftheenvironment
is obsolete and position dependent nonlinear reaction terms and diffusion ma-
triceshavetobeconsidered.Localenvironmentalpropertiesveryofteninfluence
individual survival and macroscopic persistence of species. For mathematical
results on reaction-diffusion equations in periodic media we refer to the re-