Linear stability for a periodic tumor angiogenesis model with free boundary

This paper starts with a generalized Burton, Cabrera and Frank (BCF) model by considering the energetic contribution of the adjacent terraces to the step chemical potential. We use the linear stability analysis of the quasistatic free-boundary problem for a two-dimensional step separated by broad terraces to study the step-meandering instabilities. The results show that the equilibrium adatom coverage has influence on the morphological instabilities.

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Asymptotic behavior of solutions to a tumor angiogenesis model with chemotaxis–haptotaxis

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202519500246 ◽

2019 ◽

Vol 29 (07) ◽

pp. 1387-1412 ◽

Cited By ~ 4

Author(s):

Peter Y. H. Pang ◽

Yifu Wang

Keyword(s):

Tumor Angiogenesis ◽

Asymptotic Behavior Of Solutions ◽

Time Behavior ◽

System Of Differential Equations ◽

One Dimensional ◽

Long Time ◽

Bounded Smooth ◽

The One ◽

Global Boundedness ◽

Angiogenesis Model

This paper studies the following system of differential equations modeling tumor angiogenesis in a bounded smooth domain [Formula: see text] ([Formula: see text]): [Formula: see text] where [Formula: see text] and [Formula: see text] are positive parameters. For any reasonably regular initial data [Formula: see text], we prove the global boundedness ([Formula: see text]-norm) of [Formula: see text] via an iterative method. Furthermore, we investigate the long-time behavior of solutions to the above system under an additional mild condition, and improve previously known results. In particular, in the one-dimensional case, we show that the solution [Formula: see text] converges to [Formula: see text] with an explicit exponential rate as time tends to infinity.

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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF A TUMOR ANGIOGENESIS MODEL WITH CHEMOTAXIS AND HAPTOTAXIS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202513500553 ◽

2013 ◽

Vol 24 (03) ◽

pp. 427-464 ◽

Cited By ~ 16

Author(s):

CRISTIAN MORALES-RODRIGO ◽

J. IGNACIO TELLO

Keyword(s):

Global Existence ◽

Tumor Angiogenesis ◽

Parabolic Equations ◽

Existence Of Solutions ◽

Asymptotically Stable ◽

System Of Differential Equations ◽

Homogeneous Steady State ◽

Global Existence Of Solutions ◽

Extra Assumption ◽

Angiogenesis Model

We consider a system of differential equations modeling tumor angiogenesis. The system consists of three equations: two parabolic equations with chemotactic terms to model endothelial cells and tumor angiogenesis factors coupled to an ordinary differential equation which describes the evolution of the fibronectin concentration. We study global existence of solutions and, under extra assumption on the initial data of the fibronectin concentration we obtain that the homogeneous steady state is asymptotically stable.

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Linear stability for a free boundary tumor model with a periodic supply of external nutrients

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5412 ◽

2018 ◽

Vol 42 (3) ◽

pp. 1039-1054 ◽

Cited By ~ 7

Author(s):

Yaodan Huang ◽

Zhengce Zhang ◽

Bei Hu

Keyword(s):

Free Boundary ◽

Linear Stability ◽

Tumor Model

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BÉNARD-MARANGONI FERROCONVECTION WITH FEEDBACK CONTROL

International Journal of Modern Physics Conference Series ◽

10.1142/s201019451200565x ◽

2012 ◽

Vol 09 ◽

pp. 552-559

Author(s):

NOR FADZILLAH MOHD MOKHTAR ◽

NORIHAN MD ARIFIN

Keyword(s):

Stability Analysis ◽

Feedback Control ◽

Free Boundary ◽

Galerkin Method ◽

Linear Stability ◽

Linear Stability Analysis ◽

Lower Boundary ◽

Critical Stability ◽

Stability Parameters ◽

The Galerkin Method

The effect of feedback control on the onset of Bénard-Marangoni ferroconvection in a horizontal ferrofluid layer heated from below is investigated theoretically. The lower boundary is rigid and the upper free boundary is assumed to be flat and undeformable. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is found that the onset of instability can be delayed through the use of feedback control.

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