Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: An application to a model of tumor growth

Avner Friedman; Borys Bazaliy

doi:10.1512/iumj.2003.52.2317

Global existence and asymptotic stability for an elliptic-parabolic free boundary problem: An application to a model of tumor growth

Indiana University Mathematics Journal ◽

10.1512/iumj.2003.52.2317 ◽

2003 ◽

Vol 52 (5) ◽

pp. 1265-1304 ◽

Cited By ~ 35

Author(s):

Avner Friedman ◽

Borys Bazaliy

Keyword(s):

Asymptotic Stability ◽

Free Boundary ◽

Global Existence ◽

Tumor Growth ◽

Boundary Problem ◽

Free Boundary Problem

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Asymptotic Stability of the Stationary Solution for a Hyperbolic Free Boundary Problem Modeling Tumor Growth

SIAM Journal on Mathematical Analysis ◽

10.1137/080717778 ◽

2008 ◽

Vol 40 (4) ◽

pp. 1692-1724 ◽

Cited By ~ 9

Author(s):

Shangbin Cui

Keyword(s):

Asymptotic Stability ◽

Free Boundary ◽

Tumor Growth ◽

Boundary Problem ◽

Stationary Solution ◽

Free Boundary Problem ◽

Problem Modeling

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Asymptotic Stability of the Stationary Solution for a Parabolic-Hyperbolic Free Boundary Problem Modeling Tumor Growth

SIAM Journal on Mathematical Analysis ◽

10.1137/130906271 ◽

2013 ◽

Vol 45 (5) ◽

pp. 2870-2893 ◽

Cited By ~ 9

Author(s):

Shangbin Cui

Keyword(s):

Asymptotic Stability ◽

Free Boundary ◽

Tumor Growth ◽

Boundary Problem ◽

Stationary Solution ◽

Free Boundary Problem ◽

Problem Modeling

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Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-005-0268-1 ◽

2005 ◽

Vol 21 (4) ◽

pp. 597-614 ◽

Cited By ~ 17

Author(s):

Shang-bin Cui ◽

Xue-mei Wei

Keyword(s):

Free Boundary ◽

Global Existence ◽

Tumor Growth ◽

Boundary Problem ◽

Free Boundary Problem

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A free boundary problem for necrotic tumor growth with angiogenesis

Applicable Analysis ◽

10.1080/00036811.2021.1969013 ◽

2021 ◽

pp. 1-11

Author(s):

Shihe Xu ◽

Fangwei Zhang ◽

Qinghua Zhou

Keyword(s):

Free Boundary ◽

Tumor Growth ◽

Boundary Problem ◽

Free Boundary Problem ◽

Necrotic Tumor ◽

A Free Boundary Problem

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

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2018.10.004 ◽

2019 ◽

Vol 47 ◽

pp. 106-126 ◽

Cited By ~ 3

Author(s):

Haishuang Shen ◽

Xuemei Wei

Keyword(s):

Free Boundary ◽

Tumor Growth ◽

Qualitative Analysis ◽

Boundary Problem ◽

Free Boundary Problem ◽

Problem Modeling ◽

A Free Boundary Problem

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Linear stability analysis for a free boundary problem modeling tumor growth in the presence of high-molecular mass drugs

Journal of Differential Equations ◽

10.1016/j.jde.2021.11.021 ◽

2022 ◽

Vol 309 ◽

pp. 30-73

Author(s):

Wenhua He ◽

Ruixiang Xing

Keyword(s):

Stability Analysis ◽

Free Boundary ◽

Tumor Growth ◽

Molecular Mass ◽

Boundary Problem ◽

Linear Stability ◽

Free Boundary Problem ◽

Linear Stability Analysis ◽

High Molecular Mass ◽

A Free Boundary Problem

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Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2008.09.029 ◽

2009 ◽

Vol 41 (5) ◽

pp. 2491-2494 ◽

Cited By ~ 10

Author(s):

Shihe Xu

Keyword(s):

Hopf Bifurcation ◽

Free Boundary ◽

Tumor Growth ◽

Boundary Problem ◽

Free Boundary Problem ◽

Time Delays ◽

Problem Modeling ◽

A Free Boundary Problem

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Global Existence and Asymptotic Behavior of Solutions to a Free Boundary Problem for the 1D Viscous Radiative and Reactive Gas

Acta Mathematica Sinica English Series ◽

10.1007/s10114-017-7316-7 ◽

2017 ◽

Vol 34 (5) ◽

pp. 827-842 ◽

Cited By ~ 1

Author(s):

Chang Ming Song ◽

Hong Li ◽

Jian Lin Zhang

Keyword(s):

Asymptotic Behavior ◽

Free Boundary ◽

Global Existence ◽

Boundary Problem ◽

Free Boundary Problem ◽

Asymptotic Behavior Of Solutions ◽

A Free Boundary Problem ◽

Reactive Gas

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Asymptotic Stability of Stationary Solutions of a Free Boundary Problem Modeling the Growth of Tumors with Fluid Tissues

SIAM Journal on Mathematical Analysis ◽

10.1137/080726550 ◽

2009 ◽

Vol 41 (1) ◽

pp. 391-414 ◽

Cited By ~ 13

Author(s):

Junde Wu ◽

Shangbin Cui

Keyword(s):

Asymptotic Stability ◽

Free Boundary ◽

Boundary Problem ◽

Free Boundary Problem ◽

Stationary Solutions ◽

Problem Modeling ◽

A Free Boundary Problem

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Asymptotic behavior of solutions of a free boundary problem modeling multi-layer tumor growth in presence of inhibitor

Acta Mathematica Sinica English Series ◽

10.1007/s10114-011-8361-2 ◽

2011 ◽

Vol 27 (8) ◽

pp. 1621-1636

Author(s):

Xiu Mei Hou

Keyword(s):

Asymptotic Behavior ◽

Free Boundary ◽

Tumor Growth ◽

Boundary Problem ◽

Free Boundary Problem ◽

Asymptotic Behavior Of Solutions ◽

Problem Modeling ◽

A Free Boundary Problem

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