8 citations · 12 across the 12 of their papers we have counts for
12 papers
Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis
Min-Jhe Lu, Wenrui Hao, Bei Hu +1
A considerable number of research works has been devoted to the study of tumor models. Several biophysical factors, such as cell proliferation, apoptosis, chemotaxis, angiogenesis…
Two neural-network-based methods for solving obstacle problems
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks,…
The linear stability for a free boundary problem modeling multi-layer tumor growth with time delay
Wenhua He, Ruixiang Xing, Bei Hu
We study a free boundary problem modeling multi-layer tumor growth with a small time delay , representing the time needed for the cell to complete the replication process. The m…
Convergence analysis of neural networks for solving a free boundary system
Xinyue Evelyn Zhao, Wenrui Hao, Bei Hu
Free boundary problems deal with systems of partial differential equations, where the domain boundaries are apriori unknown. Due to this special characteristic, it is challenging t…
On the first bifurcation point for a free boundary problem modeling small arterial plaque
Xinyue Evelyn Zhao, Bei Hu
Atherosclerosis occurs when plaque clogs the arteries. It is a leading cause of death in the United States and worldwide. In this paper, we study the bifurcation for a highly nonli…
Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms
Caihong Chang, Bei Hu, Zhengce Zhang
This paper is concerned with two properties of positive weak solutions of quasilinear elliptic equations with nonlinear gradient terms. First, we show a Liouville-type theorem for…
Bifurcation for a free boundary problem modeling a small arterial plaque
Xinyue Evelyn Zhao, Bei Hu
Atherosclerosis, hardening of the arteries, originates from small plaque in the arteries; it is a major cause of disability and premature death in the United States and worldwide.…
Asymptotic stability for a free boundary tumor model with angiogenesis
Yaodan Huang, Zhengce Zhang, Bei Hu
In this paper, we study a free boundary problem modeling solid tumor growth with vasculature which supplies nutrients to the tumor; this is characterized in the Robin boundary cond…
Stationary solutions of a free boundary problem modeling the growth of vascular tumors with a necrotic core
Huijuan Song, Bei Hu, Zejia Wang
In this paper, we present a rigorous mathematical analysis of a free boundary problem modeling the growth of a vascular solid tumor with a necrotic core. If the vascular system sup…
The Impact of Time Delay in a Tumor Model
Xinyue Evelyn Zhao, Bei Hu
In this paper we consider a free boundary tumor growth model with a time delay in cell proliferation and study how time delay affects the stability and the size of the tumor. The m…
A parabolic-hyperbolic system modeling the growth of a tumor
Rui Li, Bei Hu
In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix-degrading enzymes, which satisfy a coupled system of PDEs…
Analysis of a Mathematical Model of Ischemic Cutaneous wounds
Avner Friedman, Bei Hu, Chuan Xue
Chronic wounds represent a major public health problem affecting 6.5 million people in the United States. Ischemia represents a serious complicating factor in wound healing. In thi…