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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Altai State University
2024-04-01
|
| Series: | Известия Алтайского государственного университета |
| Subjects: | |
| Online Access: | http://izvestiya.asu.ru/article/view/15015 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850181628353052672 |
|---|---|
| author | Вардан Баландурович Погосян Маргарита Андреевна Токарева Александр Алексеевич Папин |
| author_facet | Вардан Баландурович Погосян Маргарита Андреевна Токарева Александр Алексеевич Папин |
| author_sort | Вардан Баландурович Погосян |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2c094e81aa3a4af0b7b50fb3c69e7279 |
| institution | OA Journals |
| issn | 1561-9443 1561-9451 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Altai State University |
| record_format | Article |
| series | Известия Алтайского государственного университета |
| spelling | doaj-art-2c094e81aa3a4af0b7b50fb3c69e72792025-08-20T02:17:52ZengAltai State UniversityИзвестия Алтайского государственного университета1561-94431561-94512024-04-011(135)13814310.14258/izvasu(2024)1-2015015Localization of Solutions to Equations of Tumor DynamicsВардан Баландурович Погосян0Маргарита Андреевна Токарева1Александр Алексеевич Папин2Altai State University, Barnaul, RussiaLavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, RussiaAltai State University, Barnaul, RussiaThis 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.http://izvestiya.asu.ru/article/view/15015differential equationsfiltrationtumorlocalizationporosity |
| spellingShingle | Вардан Баландурович Погосян Маргарита Андреевна Токарева Александр Алексеевич Папин Localization of Solutions to Equations of Tumor Dynamics Известия Алтайского государственного университета differential equations filtration tumor localization porosity |
| title | Localization of Solutions to Equations of Tumor Dynamics |
| title_full | Localization of Solutions to Equations of Tumor Dynamics |
| title_fullStr | Localization of Solutions to Equations of Tumor Dynamics |
| title_full_unstemmed | Localization of Solutions to Equations of Tumor Dynamics |
| title_short | Localization of Solutions to Equations of Tumor Dynamics |
| title_sort | localization of solutions to equations of tumor dynamics |
| topic | differential equations filtration tumor localization porosity |
| url | http://izvestiya.asu.ru/article/view/15015 |
| work_keys_str_mv | AT vardanbalandurovičpogosân localizationofsolutionstoequationsoftumordynamics AT margaritaandreevnatokareva localizationofsolutionstoequationsoftumordynamics AT aleksandralekseevičpapin localizationofsolutionstoequationsoftumordynamics |