Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

Jan Giesselmann; Niklas Kolbe; Mária Lukáčová-Medvidová; Nikolaos Sfakianakis

doi:10.3934/dcdsb.2018169

Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

Jan Giesselmann, Niklas Kolbe, Mária Lukáčová-Medvidová, Nikolaos Sfakianakis

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.

Original language	English
Pages (from-to)	4397-4431
Number of pages	35
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	23
Issue number	10
Early online date	30 Jun 2018
DOIs	https://doi.org/10.3934/dcdsb.2018169
Publication status	Published - Dec 2018

Keywords

Advection-reaction-diffusion
Cancer stem cells
Classical solutions
Haptotaxis model
Invasion of the extracellular matrix

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.3934/dcdsb.2018169

Nikolaos Sfakianakis
- n.sfakianakisst-andrews.acuk
- Applied Mathematics - Lecturer in Applied Mathematics
- Infection and Global Health Division
Person: Academic

Cite this

@article{e5b2de916a13453296f2a807d8b73f05,

title = "Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model",

abstract = "We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.",

keywords = "Advection-reaction-diffusion, Cancer stem cells, Classical solutions, Haptotaxis model, Invasion of the extracellular matrix",

author = "Jan Giesselmann and Niklas Kolbe and M{\'a}ria Luk{\'a}{\v c}ov{\'a}-Medvidov{\'a} and Nikolaos Sfakianakis",

year = "2018",

month = dec,

doi = "10.3934/dcdsb.2018169",

language = "English",

volume = "23",

pages = "4397--4431",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "10",

}

TY - JOUR

T1 - Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

AU - Giesselmann, Jan

AU - Kolbe, Niklas

AU - Lukáčová-Medvidová, Mária

AU - Sfakianakis, Nikolaos

PY - 2018/12

Y1 - 2018/12

N2 - We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.

AB - We consider a haptotaxis cancer invasion model that includes two families of cancer cells. Both families migrate on the extracellular matrix and proliferate. Moreover the model describes an epithelial-to-mesenchymal-like transition between the two families, as well as a degradation and a self-reconstruction process of the extracellular matrix. We prove in two dimensional space positivity and conditional global existence and uniqueness of the classical solutions of the problem for large initial data.

KW - Advection-reaction-diffusion

KW - Cancer stem cells

KW - Classical solutions

KW - Haptotaxis model

KW - Invasion of the extracellular matrix

U2 - 10.3934/dcdsb.2018169

DO - 10.3934/dcdsb.2018169

M3 - Article

AN - SCOPUS:85054168977

SN - 1531-3492

VL - 23

SP - 4397

EP - 4431

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 10

ER -

Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

Abstract

Keywords

UN SDGs

Access to Document

Fingerprint

Profiles

Nikolaos Sfakianakis

Cite this