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Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole Read chapter Read first chapter

2017 | OriginalPaper | Chapter

On a Diffuse Interface Model for Tumour Growth with Non-local Interactions and Degenerate Mobilities

Authors : Sergio Frigeri, Kei Fong Lam, Elisabetta Rocca

Published in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Publisher: Springer International Publishing

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Abstract

We study a non-local variant of a diffuse interface model proposed by Hawkins–Daarud et al. (Int. J. Numer. Methods Biomed. Eng. 28:3–24, 2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn–Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.

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previous chapter Nontrivial Solutions of Quasilinear Elliptic Equations with Natural Growth Term
next chapter A Boundary Control Problem for the Equation and Dynamic Boundary Condition of Cahn–Hilliard Type
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Metadata
Title
On a Diffuse Interface Model for Tumour Growth with Non-local Interactions and Degenerate Mobilities
Authors
Sergio Frigeri
Kei Fong Lam
Elisabetta Rocca
Copyright Year
2017
Book
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Print ISBN: 978-3-319-64488-2

Electronic ISBN: 978-3-319-64489-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-64489-9_9

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