Forms of travelling waves admitted by a mechanochemical model of tumour angiogenesis | Zendy

Piechór Kazimierz | Zendy

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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.

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