Thesis
Stability and Bifurcation Analysis of Applied Free Boundary Problems. PhD thesis, University of Notre Dame, June 2021. [ thesis ]
Jounral Papers
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X. E. Zhao and W. Hao, “Emergence of non-trivial solutions from trivial solutions in reaction-diffusion equations for pattern formation”, Mathematical Biosciences, 2024. [ DOI ]
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G. Webb and X. E. Zhao, “An epidemic model with infection age and vaccination age structure”, Infectious Disease Reports, 2024. [ DOI ]
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X. E. Zhao, L. Chen, W. Hao and Y. Zhao, “Bifurcation analysis reveals solution structures of phase field models”, Communications on Applied Mathematics and Computation, 2024. [ DOI | arxiv ]
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G. Webb and X. E. Zhao, “Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments“， Journal of Mathematical Biology, 2023. [ DOI ]
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X. E. Zhao, W. Hao and B. Hu, “Two neural-network-based methods for solving elliptic obstacle problems”, Chaos, Solitons and Fractals, 2022. [ DOI | arxiv ]
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X. E. Zhao and B. Hu, “On the first bifurcation point for a free boundary problem modeling a small arterial plaque”, Mathematical Methods in the Applied Sciences, 2022. [ DOI | arxiv ]
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X. E. Zhao, W. Hao and B. Hu, “Convergence analysis of neural networks for solving a free boundary problem”, Computers & Mathematics with Applications, 2021. [ DOI | arxiv ]
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X. E. Zhao and B. Hu, “Bifurcation for a free boundary problem modeling a small arterial plaque”, Journal of Differential Equations, 2021. [ DOI | arxiv ]
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X. E. Zhao and B. Hu, “Symmetry-breaking bifurcation for a free-boundary tumor model with time delay”, Journal of Differential Equations, 2021. [ DOI ]
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X. E. Zhao and B. Hu, “The impact of time delay in a tumor model”, Nonlinear Analysis: Real World Applications, 2020. [ DOI | arxiv ]
Posters
- X. E. Zhao and B. Hu, “A Free Boundary Tumor Growth Model with a Time Delay in Cell Proliferation”. [ poster ]
- X. E. Zhao, W. Hao and B. HU, “Solving a Free Boundary System by Using Neural Networks”. [ poster ]
- X. E. Zhao and G. Webb, “Bifurcation Analysis of Critical Values forWound Closure Outcomes in Wound Healing Experiments”. [ poster ]