Pattern Formation for a Reaction Diffusion System with Constant and Cross Diffusion

  • Verónica Anaya
  • Mostafa Bendahmane
  • Michel Langlais
  • Mauricio SepúlvedaEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 103)


In this work, we study a finite volume scheme for a reaction diffusion system with constant and cross diffusion modeling the spread of an epidemic disease within a host population structured with three subclasses of individuals (SIR-model). The mobility in each class is assumed to be influenced by the gradient of other classes. We establish the existence of a solution to the finite volume scheme and show convergence to a weak solution. The convergence proof is based on deriving a series of a priori estimates and using a general L p compactness criterion.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Verónica Anaya
    • 1
  • Mostafa Bendahmane
    • 2
  • Michel Langlais
    • 2
  • Mauricio Sepúlveda
    • 3
    Email author
  1. 1.Departamento de Matemática and GIMNAPUniversidad del Bío-BíoConcepciónChile
  2. 2.Institut de Mathématiques de Bordeaux UMR CNRS 5251Université Victor Segalen Bordeaux 2BordeauxFrance
  3. 3.DIM and CI2 MA, Universidad de ConcepciónEsteban Iturra s/n, Barrio UniversitarioConcepciónChile

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