On a Diffuse Interface Model for Tumour Growth with Non-local Interactions and Degenerate Mobilities
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AbstractWe 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.
All Author(s) ListSergio Frigeri, Kei Fong Lam, Elisabetta Rocca
All Editor(s) ListPierluigi Colli, Angelo Favini, Elisabetta Rocca, Giulio Schimperna, Jürgen Sprekels
Book titleSolvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
Series TitleSpringer INdAM Series
Year2017
Volume Number22
PublisherSpringer
Place of PublicationCham
Pages217 - 254
ISBN978-3-319-64488-2
eISBN978-3-319-64489-9
LanguagesEnglish-United Kingdom
KeywordsDegenerate mobility, Non-local Cahn–Hilliard equations, Singular potentials, Tumour growth, Weak solutions, Well-posedness

Last updated on 2020-24-05 at 23:42