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On a Splitting-Differentiation Process Leading to Cross-Diffusion

  • Gonzalo Galiano
  • Virginia Selgas
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

We generalize the dynamical system model proposed by Sánchez-Palencia for the splitting-differentiation process of populations to include spatial dependence. This gives rise to a family of cross-diffusion partial differential equations problems, among which we consider the segregation model proposed by Busenberg and Travis. For the one-dimensional case, we make a direct parabolic regularization of the problem to show the existence of solutions in the space of BV functions. Moreover, we introduce a Finite Element discretization of both our parabolic regularization and an alternative regularization previously proposed in the literature. Our numerical results suggest that our approach is more stable in the tricky regions where the solutions exhibit discontinuities.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversidad de OviedoOviedoSpain

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