Research 研究方向

Research Interest

My interest is on the mathematical and numerical analysis of PDEs including phase field models, free boundary problems and fluid models. This is my research statement.

Publications and preprints

published

1.   On the Spectral Gap of a Square Distance Matrix, joint with D. Li, D. Shirokoff and B. Wetton, J. Stat. Phys., 2017, 166(3-4), 1029--1035.

2.   Asymptotic Behaviour of Time Stepping Methods for Phase Field Models, joint with D. Li, K. Promislow and B. Wetton, J. Sci. Comput., 2021, 86(3), 1--34. 

3.  On a parabolic Sine-Gordon model, joint with D. Li, C. Quan and W. Yang, Numerical Mathematics: Theory, Methods and Applications., 2021, 14(4), 1068--1084.

4.  Non-uniqueness of stationary weak solutions to the surface quasi-geostrophic  equations, joint with H. Kwon and D. Li, Comm. Math. Phys., 2021, 388 (3), 1281-1295.

5. Global wellposedness for 2D quasilinear wave without Lorentz, joint with D. Li, J. Xu and D. Zha, Dynam. Part. Differ. Eq.,  2022,  19(2) ,  123-140.

6. On the equivalence of classical Helmholtz equation and fractional Helmholtz equation with arbitrary order, joint with D. Li and W. Yang , to appear in Comm. Contemp. Math.

7.  Equivalent formulations of the oxygen diffusion problem and other implicit free boundary value problems and implications for numerical approximation, joint with Z. Fu and B. Wetton, SIAM J. Appl. Math., 2023, 83(1), 52-78.

preprints

1.   On a Sinc-type MBE model, joint with D. Li, C. Quan and W. Yang, submitted. ArXiv:2106.16193.

2.  Uniform Boundedness of Highest Norm for 2D Quasilinear Wave,  joint with D. Li and J. Xu, submitted. ArXiv:2104.10019.

3. Stability analysis of BDF methods for gradient flows with $L^2$-bounded nonlinearity, joint with D. Li, C. Quan and W. Yang, preprint.

4. Energy stability and convergence of Strang splitting method for Cahn-Hilliard equation, joint with D. Li, preprint.

5. Global well-posedness for 2D quasilinear wave equations with non-compactly supported initial data, joint with D. Li and J. Xu, preprint.

6. On the global well-posedness and scattering of the 3D Klein-Gordon-Zakharov system, joint with J. Xu, submitted, arXiv:2210.13786.

7. Localization for general Helmholtz, joint with D. Li and W. Yang, arXiv:2210.03309.

8. Small global solutions to a two dimensional wave-Klein-Gordon system, preprint.

9. Energy stable semi-implicit schemes for the 2D Allen-Cahn and fractional Cahn-Hilliard equations, preprint.

Academic activities

talks:

• CSIAM 2022 @ Guangzhou, Guangdong, China                                                                     2022/11

• Workshop on Analysis and PDE @ Tianjin Center for Applied Mathematics (TCAM)       2019/08

• SIAM Conference on Applications of Dynamical Systems @ Snowbird, UT, US                2019/05

visiting:

• SUSTech, Shenzhen, China                                                                                         2021/10-2022/01

• SUSTech, Shenzhen, China                                                                                         2021/02-2021/04

• Tianjin University, Tianjin, China                                                                                2019/06-2019/07

• SUSTech, Shenzhen, China                                                                                                         2018/07

• Michigan State University, East Lansing, US                                                                            2018/04