Accepted Paper
Inserted: 16 nov 2017
Last Updated: 26 aug 2018
Journal: SIAM J. Math. An.
Year: 2018
Abstract:
One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, \emph{i.e.} population densities with disjoint supports. We analyse such a reaction cross-diffusion system in 1D. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to prove conservation of segregation for initially segregated data even in the presence of vacuum.
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