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arXiv · 1807.10431

Traveling wave solutions in a model for tumor invasion with the acid-mediation hypothesis

P. N. Davis·P. van Heijster·R. Marangell·M. R. Rodrigo
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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.

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P. N. Davis, P. van Heijster, R. Marangell, M. R. Rodrigo. 2018-07-27. Traveling wave solutions in a model for tumor invasion with the acid-mediation hypothesis. https://doi.org/10.1007/s10884-021-10003-7

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