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

Journal Article


Abstract


  • 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.

Publication Date


  • 2022

Citation


  • Davis, P. N., van Heijster, P., Marangell, R., & Rodrigo, M. R. (2022). Traveling Wave Solutions in a Model for Tumor Invasion with the Acid-Mediation Hypothesis. Journal of Dynamics and Differential Equations, 34(2), 1325-1347. doi:10.1007/s10884-021-10003-7

Scopus Eid


  • 2-s2.0-85105864510

Web Of Science Accession Number


Start Page


  • 1325

End Page


  • 1347

Volume


  • 34

Issue


  • 2

Place Of Publication


Abstract


  • 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.

Publication Date


  • 2022

Citation


  • Davis, P. N., van Heijster, P., Marangell, R., & Rodrigo, M. R. (2022). Traveling Wave Solutions in a Model for Tumor Invasion with the Acid-Mediation Hypothesis. Journal of Dynamics and Differential Equations, 34(2), 1325-1347. doi:10.1007/s10884-021-10003-7

Scopus Eid


  • 2-s2.0-85105864510

Web Of Science Accession Number


Start Page


  • 1325

End Page


  • 1347

Volume


  • 34

Issue


  • 2

Place Of Publication