On a subdiffusive tumour growth model with fractional time derivative

Marvin Fritz, Christina Kuttler, Mabel L. Rajendran, Barbara Wohlmuth, Laura Scarabosio

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20 Scopus citations

Abstract

In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply and chemotherapy. The subdiffusion of the system is modelled by a time fractional derivative in the equation governing the volume fraction of the tumour cells. The mass densities of the nutrients and the chemotherapeutic agents are modelled by reaction diffusion equations. We prove the existence and uniqueness of a weak solution to the model via the Faedo-Galerkin method and the application of appropriate compactness theorems. Lastly, we propose a fully discretized system and illustrate the effects of the fractional derivative and the influence of the fractional parameter in numerical examples.

Original languageEnglish
Pages (from-to)688-729
Number of pages42
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume86
Issue number4
DOIs
StatePublished - 1 Aug 2021

Keywords

  • Fractional time derivative
  • Mechanical deformation
  • Nonlinear partial differential equation
  • Subdiffusive tumour growth
  • Well posedness

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