{"title":"Exact Traveling Wave Solutions of One-Dimensional Models of Cancer Invasion","authors":"M. V. Shubina","doi":"10.1134/S1990478923030158","DOIUrl":null,"url":null,"abstract":"<p> In this paper, we obtain exact analytical solutions of equations of continuous\nmathematical models of tumor growth and invasion based on the model introduced by Chaplain\nand Lolas for the case of one spatial dimension. The models consist of a system of three nonlinear\nreaction–diffusion–taxis partial differential equations describing the interactions between cancer\ncells, the matrix degrading enzyme and the tissue. The obtained solutions are smooth nonnegative\nfunctions depending on the traveling wave variable with certain conditions imposed on model\nparameters.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"616 - 627"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923030158","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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