Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics

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2000
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Galiano, Gonzalo
Garzón, María L.
Jüngel, Ansgar
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A nonlinear population model with cross-diffusion terms for two competing species is studied analytically and numerically. Due to the cross diffusion terms, the problem is strongly nonlinear and so, no maximum principle generally applies. We show first the existence of weak solutions to the parabolic system in any space dimension. Then the one-dimensional stationary problem is investigated analytically and the notion of segregation is discussed. Finally, we present numerical results for the one-dimensional stationary problem underlining the effects of segregation of the species.

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ISO 690GALIANO, Gonzalo, María L. GARZÓN, Ansgar JÜNGEL, 2000. Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics
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@unpublished{Galiano2000Analy-6304,
  year={2000},
  title={Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics},
  author={Galiano, Gonzalo and Garzón, María L. and Jüngel, Ansgar}
}
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