Global existence and uniqueness of solutions for a free boundary problem modeling the growth of tumors with a necrotic core and a time delay in process of proliferation

DOI10.1155/2014/480147zbMath1407.35234OpenAlexW2156090660WikidataQ59067756 ScholiaQ59067756MaRDI QIDQ1718490

Shihe Xu, Min-Hai Huang

Publication date: 8 February 2019

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2014/480147

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Free boundary problems for PDEs (35R35) Systems biology, networks (92C42) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

A structure-preserving computational method in the simulation of the dynamics of cancer growth with radiotherapy ⋮ Dynamical behavior of cancer cell densities in two dimensional domain by the representation theory of solitons ⋮ Conciliating efficiency and dynamical consistency in the simulation of the effects of proliferation and motility of transforming growth factor \(\beta\) on cancer cells

Cites Work

• Unnamed Item
• Analysis of a solid avascular tumor growth model with time delays in proliferation process
• Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core
• Analysis of a delayed free boundary problem for tumor growth
• Time delay in necrotic core formation
• Solid tumour growth analysis of necrotic core formation
• Modelling the internalization of labelled cells in tumour spheroids
• Hopf bifurcation in a solid avascular tumour growth model with two discrete delays
• 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
• Numerical algorithm for the growth of human tumor cells and their responses to therapy
• Growth of necrotic tumors in the presence and absence of inhibitors
• Growth of nonnecrotic tumors in the presence and absence of inhibitors
• Nonlinear simulation of the effect of microenvironment on tumor growth
• 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
• A mathematical model of the immersion of a spherical tumor with a necrotic core into a nutrient bath
• 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
• Stationary Solutions of a Model for the Growth of Tumors and a Connection between the Nonnecrotic and Necrotic Phases
• Models for the Growth of a Solid Tumor by Diffusion

This page was built for publication: Global existence and uniqueness of solutions for a free boundary problem modeling the growth of tumors with a necrotic core and a time delay in process of proliferation