Exact Traveling Wave Solutions of One-Dimensional Models of Cancer Invasion
In this paper, we obtain exact analytical solutions of equations of continuous mathematical models of tumor growth and invasion based on the model introduced by Chaplain and Lolas for the case of one spatial dimension. The models consist of a system of three nonlinear reaction–diffusion–taxis partia...
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| Veröffentlicht in: | Journal of applied and industrial mathematics 2023-09, Vol.17 (3), p.616-627 |
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| container_title | Journal of applied and industrial mathematics |
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| creator | Shubina, M. V. |
| description | In this paper, we obtain exact analytical solutions of equations of continuous mathematical models of tumor growth and invasion based on the model introduced by Chaplain and Lolas for the case of one spatial dimension. The models consist of a system of three nonlinear reaction–diffusion–taxis partial differential equations describing the interactions between cancer cells, the matrix degrading enzyme and the tissue. The obtained solutions are smooth nonnegative functions depending on the traveling wave variable with certain conditions imposed on model parameters. |
| doi_str_mv | 10.1134/S1990478923030158 |
| format | Article |
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The obtained solutions are smooth nonnegative functions depending on the traveling wave variable with certain conditions imposed on model parameters.</description><identifier>ISSN: 1990-4789</identifier><identifier>EISSN: 1990-4797</identifier><identifier>DOI: 10.1134/S1990478923030158</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Cancer ; Exact solutions ; Mathematical models ; Mathematics ; Mathematics and Statistics ; One dimensional models ; Partial differential equations ; Traveling waves</subject><ispartof>Journal of applied and industrial mathematics, 2023-09, Vol.17 (3), p.616-627</ispartof><rights>Pleiades Publishing, Ltd. 2023</rights><rights>Pleiades Publishing, Ltd. 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c1838-5d37d2a9ec90c95518858d26511d64badab2bfdfc9e78c8e3f968c0041d437503</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1990478923030158$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1990478923030158$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Shubina, M. V.</creatorcontrib><title>Exact Traveling Wave Solutions of One-Dimensional Models of Cancer Invasion</title><title>Journal of applied and industrial mathematics</title><addtitle>J. Appl. Ind. Math</addtitle><description>In this paper, we obtain exact analytical solutions of equations of continuous mathematical models of tumor growth and invasion based on the model introduced by Chaplain and Lolas for the case of one spatial dimension. The models consist of a system of three nonlinear reaction–diffusion–taxis partial differential equations describing the interactions between cancer cells, the matrix degrading enzyme and the tissue. The obtained solutions are smooth nonnegative functions depending on the traveling wave variable with certain conditions imposed on model parameters.</description><subject>Cancer</subject><subject>Exact solutions</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>One dimensional models</subject><subject>Partial differential equations</subject><subject>Traveling waves</subject><issn>1990-4789</issn><issn>1990-4797</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1UMtKAzEUDaJgqf0AdwHXozfJ5LWUWrWodNGKyyGTZMrINKlJW_TvnVrRhbi6h_PichA6J3BJCCuv5kRrKKXSlAEDwtURGuypopRaHv9gpU_RKOe2BkaoYELQAXqYvBu7wYtkdr5rwxK_9ADPY7fdtDFkHBs8C764aVc-5J4xHX6KzndfytgE6xOehp3Za2fopDFd9qPvO0TPt5PF-L54nN1Nx9ePhSWKqYI7Jh012lsNVnNOlOLKUcEJcaKsjTM1rRvXWO2lssqzRgtlAUriSiY5sCG6OPSuU3zb-rypXuM29a_liiolQAJI2bvIwWVTzDn5plqndmXSR0Wg2s9W_Zmtz9BDJvfesPTpt_n_0CesKG17</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Shubina, M. V.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope></search><sort><creationdate>20230901</creationdate><title>Exact Traveling Wave Solutions of One-Dimensional Models of Cancer Invasion</title><author>Shubina, M. 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| subjects | Cancer Exact solutions Mathematical models Mathematics Mathematics and Statistics One dimensional models Partial differential equations Traveling waves |
| title | Exact Traveling Wave Solutions of One-Dimensional Models of Cancer Invasion |
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