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Global existence of classical solutions and numerical simulations of a cancer invasion model

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10473254" target="_blank" >RIV/00216208:11320/23:10473254 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.jY-SWgSHY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.jY-SWgSHY</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1051/m2an/2023037" target="_blank" >10.1051/m2an/2023037</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Global existence of classical solutions and numerical simulations of a cancer invasion model

  • Original language description

    In this paper, we study a cancer invasion model both theoretically and numerically. The model is a nonstationary, nonlinear system of three coupled partial differential equations modeling the motion of cancer cells, degradation of the extracellular matrix, and certain enzymes. We first establish existence of global classical solutions in both two- and three-dimensional bounded domains, despite the lack of diffusion of the matrix-degrading enzymes and corresponding regularizing effects in the analytical treatment. Next, we give a weak formulation and apply finite differences in time and a Galerkin finite element scheme for spatial discretization. The overall algorithm is based on a fixed-point iteration scheme. Our theory and numerical developments are accompanied by some simulations in two and three spatial dimensions.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

    <a href="/en/project/GA22-01591S" target="_blank" >GA22-01591S: Mathematical theory and numerical analysis for equations of viscous newtonian compressible fluids</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2023

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Mathematical Modelling and Numerical Analysis

  • ISSN

    0764-583X

  • e-ISSN

    2804-7214

  • Volume of the periodical

    57

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    FR - FRANCE

  • Number of pages

    27

  • Pages from-to

    1893-1919

  • UT code for WoS article

    001020856600002

  • EID of the result in the Scopus database

    2-s2.0-85164539710