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

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Book cover Numerical Mathematics and Advanced Applications - ENUMATH 2013

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

Abstract

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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References

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Author information

Authors and Affiliations

  1. Departamento de Matemática and GIMNAP, Universidad del Bío-Bío, Concepción, Chile

    Verónica Anaya

  2. Institut de Mathématiques de Bordeaux UMR CNRS 5251, Université Victor Segalen Bordeaux 2, Bordeaux, France

    Mostafa Bendahmane & Michel Langlais

  3. DIM and CI2 MA, Universidad de Concepción, Esteban Iturra s/n, Barrio Universitario, Concepción, Chile

    Mauricio Sepúlveda

Authors
  1. Verónica Anaya
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  2. Mostafa Bendahmane
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  3. Michel Langlais
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  4. Mauricio Sepúlveda
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Corresponding author

Correspondence to Mauricio Sepúlveda .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

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Anaya, V., Bendahmane, M., Langlais, M., Sepúlveda, M. (2015). Pattern Formation for a Reaction Diffusion System with Constant and Cross Diffusion. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_15

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