A qualitative analysis of a free boundary problem modeling tumor growth with angiogenesis

DOI10.1016/j.nonrwa.2018.10.004zbMath1414.35244OpenAlexW2902579448WikidataQ128968423 ScholiaQ128968423MaRDI QIDQ1729255

Xuemei Wei, Haishuang Shen

Publication date: 27 February 2019

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2018.10.004

zbMATH Keywords

asymptotic behaviorangiogenesistumor growthfree boundary problemglobal solutionstationary solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell biology (92C37) Free boundary problems for PDEs (35R35) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Analysis of a time-delayed free boundary problem for solid tumor growth with angiogenesis and direct influence of inhibitors ⋮ A free boundary problem for necrotic tumor growth with angiogenesis ⋮ Linear stability analysis for the free boundary problem modeling tumor growth with angiogenesis in the presence of inhibitors ⋮ Analysis of a free boundary problem for vascularized tumor growth with a necrotic core and time delays ⋮ Analysis of a tumor model free boundary problem with action of an inhibitor and nonlinear boundary conditions ⋮ Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core ⋮ Analysis of necrotic core formation in angiogenic tumor growth ⋮ A parabolic-hyperbolic system modeling the tumor growth with angiogenesis ⋮ Analysis of a tumor-model free boundary problem with a nonlinear boundary condition

Cites Work

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• Analysis of a free-boundary tumor model with angiogenesis
• Existence of a stationary solution for the modified Ward-King tumor growth model
• Analysis of a mathematical model for the growth of tumors
• Analysis of a mathematical model of protocell
• A hyperbolic free boundary problem modeling tumor growth
• A hierarchy of cancer models and their mathematical challenges
• Analysis of a mathematical model for the growth of tumors under the action of external inhibitors
• Analysis of a model of a virus that replicates selectively in tumor cells
• Growth of nonnecrotic tumors in the presence and absence of inhibitors
• Asymptotic behavior of solutions of a free-boundary tumor model with angiogenesis
• Global existence of solutions for a free boundary problem modeling the growth of necrotic tumors
• Formation of necrotic cores in the growth of tumors: analytic results
• Asymptotic stability for a free boundary problem arising in a tumor model
• Global existence for a parabolic-hyperbolic free boundary problem modelling tumor growth
• Analysis of a free boundary problem modeling tumor growth
• Asymptotic Stability of the Stationary Solution for a Parabolic-Hyperbolic Free Boundary Problem Modeling Tumor Growth
• A free boundary problem for a singular system of differential equations: An application to a model of tumor growth
• A Free Boundary Problem for an Elliptic-Hyperbolic System: An Application to Tumor Growth
• A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior
• Analysis of a mathematical model of the growth of necrotic tumors