A coupled Cahn–Hilliard model for the proliferative-to-invasive transition of hypoxic glioma cells | Zendy

Lu Li | Zendy; Alain Miranville | Zendy; Rémy Guillevin | Zendy

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A coupled Cahn–Hilliard model for the proliferative-to-invasive transition of hypoxic glioma cells

Author(s) -

Lu Li,

Alain Miranville,

Rémy Guillevin

Publication year - 2020

Publication title -

quarterly of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.603

H-Index - 41

eISSN - 1552-4485

pISSN - 0033-569X

DOI - 10.1090/qam/1585

Subject(s) - cahn–hilliard equation , logarithm , chemical equation , nonlinear system , glioma , coupling (piping) , diffusion equation , mathematics , mathematical analysis , physics , chemistry , partial differential equation , materials science , medicine , quantum mechanics , cancer research , economy , economics , metallurgy , service (business)

Our aim in this paper is to prove the existence of solutions for a model for the proliferative-to-invasive transition of hypoxic glioma cells. The equations consist of the coupling of a reaction-diffusion equation for the tumor density and of a Cahn–Hilliard type equation for the oxygen concentration. The main difficulty is to prove the existence of a biologically relevant solution. This is achieved by considering a modified equation and taking a logarithmic nonlinear term in the Cahn–Hilliard equation.

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