On the long term spatial segregation for a competition-diffusion system

Details On the long term spatial segregation for a competition-diffusion system On the long term spatial segregation for a competition-diffusion system

2008-06-05

arxiv.org/abs/0806.0969v1

Asymptotic Anal. 57 (2008), 83-103

Mathematics

Analysis of PDEs

16 pages

Scientific paper

We investigate the long term behavior for a class of competition-diffusion systems of Lotka-Volterra type for two competing species in the case of low regularity assumptions on the data. Due to the coupling that we consider the system cannot be reduced to a single equation yielding uniform estimates with respect to the inter-specific competition rate parameter. Moreover, in the particular but meaningful case of initial data with disjoint support and Dirichlet boundary data which are time-independent, we prove that as the competition rate goes to infinity the solution converges, along with suitable sequences, to a spatially segregated state satisfying some variational inequalities.

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