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 language | English |
|---|---|
| Pages (from-to) | 688–729 |
| Number of pages | 42 |
| Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |
| Volume | 86 |
| Issue number | 4 |
| Early online date | 8 Jun 2021 |
| DOIs | |
| Publication status | Published - Aug 2021 |
| Externally published | Yes |
Bibliographical note
Funding:Deutsche Forschungsgemeinschaft (DFG) through TUM International Graduate School of Science and Engineering (GSC 81); Laura Bassi Postdoctoral Fellowship (Technical University of Munich; to M.L.R.); and DFG (WO-671 11-1 to M.F., L.S. and B.W.).
Keywords
- subdiffusive tumour growth
- mechanical deformations
- fractional time derivative
- nonlinear partial differential equation
- well posedness