Ph.D. The Ohio State University, 2000

M.S. Huazhong University of Science and Technology, 1986

B.S. Huazhong University of Science and Technology, 1984

Research Interest:

Mathematical analysis and simulation of models for diseases such as diabetes, atherosclerosis, Free boundary problems arising in a variety of physical  and biological contexts such as Hele-Shaw flow, dendritic growth and tumor growth. Ordinary and partial differential Equations. Stochastic differential equations.

Selected Publications:

• Xie, Steady solution and its stability of a mathematical model of diabetic atherosclerosis, Journal of biological dynamics, 17:1 (2023), Article: 2257734.
• Xie, Well-posedness of a mathematical model for diabetic atherosclerosis, J. Math. Anal. Appl. 505 (2022), no. 2, Paper No. 125606, 18 pp.
• Xie, Analytic solution to an interfacial flow with kinetic undercooling in a time-dependent gap Hele-Shaw cell. Discrete & Continuous Dynamical Systems - B,26 (2021), 4663-4680.
• Xie, Rigorous results in existence and selection of Saffman-Taylor fingers by kinetic undercooling, European J. Applied Math. (2019), vol. 30, pp. 63-116.
• Xie, Existence and uniqueness of analytic solution for Rayleigh-Taylor problem, Journal of Differential Equations, 237 (2007) 116-13.
• Tanveer, X. Xie; Analyticity and nonexistence of classical steady Hele-Shaw fingers, Communications on pure and applied mathematics, Vol. 56, no 3, 353-402 (2003)
• Xie, S. Tanveer, Rigorous results in steady finger selection in viscous fingering, Archive for rational mechanics and analysis, 166 (2003) 3, 219-286.