Traveling Wave Solutions in a Model for Tumor Invasion with the Acid-Mediation Hypothesis

Paige N. Davis*, Peter van Heijster, Robert Marangell, Marianito R. Rodrigo

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)


In this manuscript, we prove the existence of slow and fast traveling wave solutions in the original Gatenby–Gawlinski model. We prove the existence of a slow traveling wave solution with an interstitial gap. This interstitial gap has previously been observed experimentally, and here we derive its origin from a mathematical perspective. We give a geometric interpretation of the formal asymptotic analysis of the interstitial gap and show that it is determined by the distance between a layer transition of the tumor and a dynamical transcritical bifurcation of two components of the critical manifold. This distance depends, in a nonlinear fashion, on the destructive influence of the acid and the rate at which the acid is being pumped.

Original languageEnglish
Pages (from-to)1325-1347
JournalJournal of Dynamics and Differential Equations
Issue number2
Early online date12 May 2021
Publication statusPublished - Jun 2022


  • Acid-mediation hypothesis
  • Dynamical transcritical bifurcation
  • Gatenby–Gawlinski model
  • Geometric singular perturbation theory
  • Interstitial gap
  • Warburg effect


Dive into the research topics of 'Traveling Wave Solutions in a Model for Tumor Invasion with the Acid-Mediation Hypothesis'. Together they form a unique fingerprint.

Cite this