My Google Scholar Profile

Thesis

Stability and Bifurcation Analysis of Applied Free Boundary Problems. PhD thesis, University of Notre Dame, June 2021. [ thesis ]

Jounral Papers

1. X. E. Zhao, Y. Wu, R. Leander, W. Ding and S. Lenhart, Optimal control of treatment in a free boundary problem modeling multilayered tumor growth, 2024. [ arXiv ]

2. Y. Wu, X. E. Zhao, R. Leander and W. Ding, Optimal control for a free boundary tumor growth model, 2024. [ SSRN ]

3. X. E. Zhao, Analysis and optimization of tumor inhibitor treatments in a free boundary tumor growth model, Nonlinear Analysis: Real World Applications, 2025. [ DOI ]

4. X. E. Zhao and J. Shi, On determination of the bifurcation type for a free boundary problem modeling tumor growth, Journal of Differential Equations, 2025. [ DOI | arXiv ]

5. 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 ]

6. G. Webb and X. E. Zhao, An epidemic model with infection age and vaccination age structure, Infectious Disease Reports, 2024. [ DOI ]

7. 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 ]

8. 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 ]

9. 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 ]

10. 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 ]

11. 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 ]

12. X. E. Zhao and B. Hu, Bifurcation for a free boundary problem modeling a small arterial plaque, Journal of Differential Equations, 2021. [ DOI | arXiv ]

13. X. E. Zhao and B. Hu, Symmetry-breaking bifurcation for a free-boundary tumor model with time delay, Journal of Differential Equations, 2021. [ DOI ]

14. 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 ]