A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

DOI10.1142/S0218202510004428zbMath1203.35014OpenAlexW2059043856MaRDI QIDQ3573105

Verónica Anaya, Mostafa Bendahmane, Mauricio Sepúlveda

Publication date: 30 June 2010

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202510004428

zbMATH Keywords

weak solutionexistencepattern formationreaction-diffusion systemfinite volume schemehomogeneous Neumann boundary conditionscancer dynamicstwo equations in 3D

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Theoretical approximation in context of PDEs (35A35) Weak solutions to PDEs (35D30) General biology and biomathematics (92B05) Semilinear parabolic equations (35K58) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)

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Cites Work

• Mathematical model of tumor invasion along linear or tubular structures
• Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
• Convergence of a finite volume scheme for the bidomain model of cardiac tissue
• Compact sets in the space \(L^ p(0,T;B)\)
• A free boundary problem model of ductal carcinoma in situ
• The steady state of a tumor cord cell population.
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
• Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
• CELLULAR AUTOMATON MODELS OF TUMOR DEVELOPMENT: A CRITICAL REVIEW
• The chemical basis of morphogenesis
• A Free Boundary Problem with Unilateral Constraints Describing the Evolution of a Tumor Cord Under the Influence of Cell Killing Agents
• MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION
• Cancer Modelling and Simulation
• MULTICELLULAR BIOLOGICAL GROWING SYSTEMS: HYPERBOLIC LIMITS TOWARDS MACROSCOPIC DESCRIPTION
• MODELLING OF EARLY LUNG CANCER PROGRESSION: INFLUENCE OF GROWTH FACTOR PRODUCTION AND COOPERATION BETWEEN PARTIALLY TRANSFORMED CELLS
• MATHEMATICAL METHODS AND TOOLS OF KINETIC THEORY TOWARDS MODELLING COMPLEX BIOLOGICAL SYSTEMS
• A MATHEMATICAL MODEL FOR TUMOR CORDS INCORPORATING THE FLOW OF INTERSTITIAL FLUID
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