Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients

DOI10.3934/dcdsb.2016.21.997zbMath1333.35304OpenAlexW2526945984MaRDI QIDQ908171

Shihe Xu, Meng Bai, Yinhui Chen

Publication date: 3 February 2016

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2016.21.997

zbMATH Keywords

asymptotic behaviorfree boundary problemglobal solutionperiodic solutiontumors

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Periodic solutions to PDEs (35B10) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell biology (92C37) Free boundary problems for PDEs (35R35)

Related Items (6)

On a moving boundary problem associated with the swelling drug release platforms ⋮ Analysis of a nonautonomous free boundary tumor model with infinite time delays ⋮ Analysis of a free boundary problem modeling the growth of multicell spheroids with angiogenesis ⋮ Analysis of a mathematical model for tumor growth with Gibbs-Thomson relation ⋮ Analysis of a free boundary problem for tumor growth with Gibbs-Thomson relation and time delays ⋮ A free boundary tumor model with time dependent nutritional supply

Cites Work

• A history of the study of solid tumour growth: the contribution of mathematical modelling
• Analysis of a solid avascular tumor growth model with time delays in proliferation process
• Qualitative analysis of a delayed free boundary problem for tumor growth under the effect of inhibitors
• Analysis of a delayed free boundary problem for tumor growth
• Time delay in necrotic core formation
• Solid tumour growth analysis of necrotic core formation
• Hopf bifurcation in a solid avascular tumour growth model with two discrete delays
• Analysis of tumor growth under direct effect of inhibitors with time delays in proliferation
• Analysis of a mathematical model for the growth of tumors
• The effect of time delays on the dynamics of avascular tumor growth
• Time delays in proliferation process for solid avascular tumour
• Analysis of a mathematical model of the effect of inhibitors on the growth of tumors
• Analysis of a mathematical model for the growth of tumors under the action of external inhibitors
• A time delay model of tumour-immune system interactions: global dynamics, parameter estimation, sensitivity analysis
• Growth of necrotic tumors in the presence and absence of inhibitors
• Growth of nonnecrotic tumors in the presence and absence of inhibitors
• Formation of necrotic cores in the growth of tumors: analytic results
• Interactions between the immune system and cancer: A brief review of non-spatial mathematical models
• The ecology and evolutionary biology of cancer: a review of mathematical models of necrosis and tumor cell diversity
• Analysis of a free boundary problem modeling tumor growth
• Analysis of mathematical models for the growth of tumors with time delays in cell proliferation
• Asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with fluid-like tissue under the action of inhibitors
• Analyticity of solutions to a multidimensional moving boundary problem modelling tumour growth
• Models for the Growth of a Solid Tumor by Diffusion
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients