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SUMMARY:A subdiffusive tumour growth model with fractional time derivative
  - Mabel Lizzy Rajendran (University of Birmingham)
DTSTART:20240904T153000Z
DTEND:20240904T155000Z
UID:TALK219145@talks.cam.ac.uk
DESCRIPTION:Cancer growth and spread are complex processes involving nonlo
 cal phenomena such as memory and interactions with the surrounding environ
 ment. Including these phenomena in the mathematical model results in parti
 al differential equation (PDE) with nonlocal operators\, which pose intere
 sting challenges in demonstrating their well-posedness and in numerical si
 mulation.\nIn this work\, we present and analyse a system of coupled parti
 al 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 derivati
 ve in the equation governing the volume fraction of the tumour cells. The 
 mass densities of the nutrients and the chemotherapeutic agents are modell
 ed by reaction diffusion equations. The existence and uniqueness of a weak
  solution to the model is obtained via the Faedo--Galerkin method and the 
 application of appropriate compactness theorems. Lastly\, we propose a ful
 ly discretised system and illustrate the effects of the fractional derivat
 ive and the influence of the fractional parameter in numerical examples.
LOCATION:Seminar Room 1\, Newton Institute
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