On a subdiffusive tumour growth model with fractional time derivative
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 eq...
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| Published in | IMA journal of applied mathematics Vol. 86; no. 4; pp. 688 - 729 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Oxford University Press
01.08.2021
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Rajendran, Mabel L Scarabosio, Laura Wohlmuth, Barbara Fritz, Marvin Kuttler, Christina |
| Author_xml | – sequence: 1 givenname: Marvin surname: Fritz fullname: Fritz, Marvin – sequence: 2 givenname: Christina surname: Kuttler fullname: Kuttler, Christina – sequence: 3 givenname: Mabel L surname: Rajendran fullname: Rajendran, Mabel L email: rajendrm@ma.tum.de – sequence: 4 givenname: Barbara surname: Wohlmuth fullname: Wohlmuth, Barbara – sequence: 5 givenname: Laura surname: Scarabosio fullname: Scarabosio, Laura |
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| Copyright | The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. 2021 |
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| Keywords | mechanical deformation subdiffusive tumour growth nonlinear partial differential equation well posedness fractional time derivative |
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In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of... In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion,... |
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| Title | On a subdiffusive tumour growth model with fractional time derivative |
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