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Mathematical Analysis and Numerical Simulations for a System Modeling Acid-Mediated Tumor Cell Invasion

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  • Christian Märkl
  • Gülnihal Meral
  • Christina Surulescu

Abstract

This work is concerned with the mathematical analysis of a model proposed by Gatenby and Gawlinski (1996) in order to support the hypothesis that tumor-induced alteration of microenvironmental pH may provide a simple but comprehensive mechanism to explain cancer invasion. We give an intuitive proof for the existence of a solution under general initial conditions upon using an iterative approach. Numerical simulations are also performed, which endorse the predictions of the model when compared with experimentally observed qualitative facts.

Suggested Citation

  • Christian Märkl & Gülnihal Meral & Christina Surulescu, 2013. "Mathematical Analysis and Numerical Simulations for a System Modeling Acid-Mediated Tumor Cell Invasion," International Journal of Analysis, Hindawi, vol. 2013, pages 1-15, March.
    • Handle: RePEc:hin:ijanal:878051
    DOI: 10.1155/2013/878051
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