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On a Cahn–Hilliard–Darcy System for Tumour Growth with Solution Dependent Source Terms

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Trends in Applications of Mathematics to Mechanics

Part of the book series: Springer INdAM Series ((SINDAMS,volume 27))

Abstract

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn–Hilliard–Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn–Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered for the pressure variable, which allow for the source terms to be dependent on the solution variables.

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Authors and Affiliations

  1. Universität Regensburg, Regensburg, Germany

    Harald Garcke & Kei Fong Lam

Authors
  1. Harald Garcke
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  2. Kei Fong Lam
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Corresponding author

Correspondence to Harald Garcke .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica “F. Casorati”, Università degli Studi di Pavia, Pavia, Pavia, Italy

    Elisabetta Rocca

  2. Fakultät für Mathematik, Universität Wien, Wien, Austria

    Ulisse Stefanelli

  3. CNRS, Paris, Paris, France

    Lev Truskinovsky

  4. Dipartimento di Matematica, Università degli Studi di Trento, Povo di Trento, Trento, Italy

    Augusto Visintin

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Garcke, H., Lam, K.F. (2018). On a Cahn–Hilliard–Darcy System for Tumour Growth with Solution Dependent Source Terms. In: Rocca, E., Stefanelli, U., Truskinovsky, L., Visintin, A. (eds) Trends in Applications of Mathematics to Mechanics. Springer INdAM Series, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-319-75940-1_12

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