Localization of Solutions to Equations of Tumor Dynamics
This article discusses a mathematical model of tumor dynamics. The tissue is considered as a multiphase three-component medium consisting of extracellular matrix, tumor cells, and extracellular fluid. The extracellular matrix is generally deformable. In the case of the predominant extracellular flui...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Altai State University
2024-04-01
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| Series: | Известия Алтайского государственного университета |
| Subjects: | |
| Online Access: | http://izvestiya.asu.ru/article/view/15015 |
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| Summary: | This article discusses a mathematical model of tumor dynamics. The tissue is considered as a multiphase three-component medium consisting of extracellular matrix, tumor cells, and extracellular fluid. The extracellular matrix is generally deformable. In the case of the predominant extracellular fluid — tumor cell interaction, the original system of equations is reduced to the one parabolic equation degenerating on the solution with a special right-hand side. The property of a finite perturbation propagation velocity for tumor cell saturation is revealed. The introduction describes the essence of the problem. The second part presents the derivation of a mathematical model of tumor dynamics as a three-phase medium. The third part describes a mathematical model for the case when mechanical interaction with extracellular fluid is neglected. The fourth part considers the case of predominant fluid-cell interaction. The fifth part provides a proof of the theorem on the localization of the solution to the equation for the saturation of tumor cell. |
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| ISSN: | 1561-9443 1561-9451 |