Travelling wave solutions to a haptotaxis-dominated model of malignant invasion
نویسندگان
چکیده
منابع مشابه
Travelling wave solutions to a haptotaxis-dominated model of malignant invasion
A haptotaxis-dominated model of cell invasion is considered for small cell diffusion and fast protease adjustment to the cell–collagen matrix interaction. A simplified limit model has travelling wave cell invasion profiles that are blunt, that is end with a ‘shock-like’ step, and that evolve stably from initial data that lie to one side of some initial plane. In common with diffusiondominated s...
متن کاملExistence of Travelling Wave Solutions for a Model of Tumour Invasion
The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can th...
متن کاملA Review of Travelling Wave Solutions
In this paper we review the existence of diierent types of travelling wave solutions u(x; t) = (x ? ct) of degenerate non-linear reaction-diiusion equations of the form u t = D(u)u x ] x + g(u) for diierent density-dependent diiusion coeecients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diius...
متن کاملOn travelling wave solutions of the diffusive Leslie-Gower model
We investigate the diffusive Leslie–Gower predator–prey model. Travelling wave solutions were found and a minimum wave speed relationship was derived. Linear stability analysis was performed in addition to full numerical simulation of the model. All travelling waves were found to be stable. © 2015 Elsevier Inc. All rights reserved.
متن کاملTravelling Wave Solutions for a Balance Law
We study entropy travelling wave solutions for rst order hyperbolic balance laws. Results concerning existence, regularity and asymptotic stability of such solutions are proved for convex uxes and source terms with simple isolated zeros.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 2001
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/14/6/313