Premium
Forms of travelling waves admitted by a mechanochemical model of tumour angiogenesis
Author(s) -
Piechór Kazimierz
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1262
Subject(s) - uniqueness , mathematics , traveling wave , monotonic function , angiogenesis , vasculogenesis , traction (geology) , partial differential equation , mathematical analysis , endothelial stem cell , medicine , geology , chemistry , cancer research , biochemistry , geomorphology , in vitro
We study the existence and the properties of travelling wave solutions in a system of non‐linear partial differential equations, which arise in some mechanochemical models of angiogenesis and/or vasculogenesis. Under the ‘weak traction’ assumption we prove the existence and uniqueness (up to a translation) of solutions. We show the positiveness of the endothelial cell density and determine its asymptotic behaviour; also we show that the TAF concentration function is positive and monotonic. Copyright © 2010 John Wiley & Sons, Ltd.