2 citations · 2 across the 6 of their papers we have counts for
6 papers
Bifurcation Analysis Reveals Solution Structures of Phase Field Models
Xinyue Evelyn Zhao, Long-Qing Chen, Wenrui Hao +1
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new ana…
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,…
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…
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.…
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…