Mathematical models of tumour angiogenesis

DOI10.1016/j.cam.2006.04.027zbMath1109.92019OpenAlexW1993957083MaRDI QIDQ879409

Akisato Kubo, Takashi Suzuki

Publication date: 11 May 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.04.027

zbMATH Keywords

collapsetumour angiogenesisAnderson-Chaplain modelOthmer-Stevens modelparabolic ODE system

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) PDEs of mixed type (35M10) Ill-posed problems for PDEs (35R25)

Related Items

On a parabolic-elliptic system with chemotaxis and logistic type growth, On a parabolic-ODE system of chemotaxis, On a Parabolic-ODE chemotaxis system with periodic asymptotic behavior, Unnamed Item, Unnamed Item, Effect of treatment on the global dynamics of delayed pathological angiogenesis models, Global existence and asymptotic behaviour of solutions for nonlinear evolution equations related to a tumour invasion model

Cites Work

• A mathematical model for capillary network formation in the absence of endothelial cell proliferation
• Continuous and discrete mathematical models of tumor-induced angiogenesis
• A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation
• Asymptotic behavior of the solution to a parabolic ODE system modeling tumour growth.
• Partial differential equations of chemotaxis and angiogenesis
• On Existence of Global Solutions and Blow-Up to a System of Reaction-Diffusion Equations Modelling Chemotaxis
• A System of Reaction Diffusion Equations Arising in the Theory of Reinforced Random Walks
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
• Reinforced random walk