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

@inproceedings{Frigeri2017OnAD, title={On a Diffuse Interface Model for Tumour Growth with Non-local Interactions and Degenerate Mobilities}, author={Sergio Frigeri and Kei Fong Lam and Elisabetta Rocca}, year={2017} }

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…

## 33 Citations

Strong well-posedness and inverse identification problem of a non-local phase field tumour model with degenerate mobilities

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Asymptotic analysis of a tumor growth model with fractional operators

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Numerical analysis for a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport

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A fully-discrete finite element approximation of the model for tumour growth in the presence of a nutrient which is consumed by the tumour is introduced and stability bounds for the discrete scheme are proved.

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Phase field models recently gained a lot of interest in the context of tumour growth models. In this work we study several diffuse interface models for tumour growth in a bounded domain with…

Cahn-Hilliard-Brinkman model for tumor growth with possibly singular potentials

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- 2022

We analyze a phase ﬁeld model for tumor growth consisting of a Cahn–Hilliard– Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diﬀusion equation for a…

Optimal control of time and therapy in a tumor growth model with possibly singular potentials

- Physics
- 2019

A distributed optimal control problem for a diffuse interface model which physical context is that of tumor growth dynamics is discussed. The system we deal with consists of a Cahn-Hilliard equation…

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