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

Autor:	Davis, P. N., van Heijster, P., Marangell, R., Rodrigo, M. R.
Rok vydání:	2018
Předmět:	Mathematics - Analysis of PDEs Mathematics - Dynamical Systems 35Q92 35C07 35B25 92C17
Druh dokumentu:	Working Paper
DOI:	10.1007/s10884-021-10003-7
Popis:	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. Comment: 31 page, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1807.10431 Zobrazit plný text záznamu View this record from Arxiv