Publication list

1. Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces, with J.-G. Liu and J. Lu, Journal of Nonlinear Science 27 (3), 873-926, (2017).

2. Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime,with J.-G. Liu and J. Lu,   SIAM Journal on Mathematical Analysis 49 (3), 1705-1731, (2017).

3. Maximal monotone operator in non-reflexive Banach space and the application to thin film equation in epitaxial growth on vicinal surface with J.-G. Liu, X. Y. Lu and X. Xu,  Calculus of Variations and Partial Differential Equations, 57(2), (2018). 

4. Global existence of solutions to a tear film model with locally elevated evaporation rateswith H. Ji, J.-G. Liu and T. P. Witelski,    Physica D: Nonlinear Phenomena 350, 13-25, (2017). 

5. Observability inequality and decay rate for wave equations with nonlinear boundary conditions, with  J. Liang and T.-J. Xiao,    Electronic Journal of Differential Equations (161), 1-12, (2017).  

6. A new method to obtain uniform decay rates for multidimensional wave equations with nonlinear acoustic boundary conditions with J. Liang and T.-J. Xiao,  SIAM J. Control Optim., 56(2), 1303-1320, (2018). 

7. A vicinal surface model for epitaxial growth with logarithmic free energy, with H. Ji, J.-G. Liu and T. P. Witelski, Discrete Contin. Dyn. Syst. Ser. B. 23(10), 4433-4453, (2018).

8. Determination of harmonic parameters with temporal variations: An enhanced harmonic analysis algorithm and application to internal tidal currents in the South China Sea with G. Jin, H. Pan, Q. Zhang, X. Lv and W. Zhao,  J. Atmospheric Ocean. Technol., 35(7): 1375-1398, (2018). 

9. Gradient flow approach to an exponential thin film equation: global existence and latent singularity with J.-G. Liu and X. Y. Lu,  ESIAM Control Optim. Calc. Var., 25:49, (2019). 

10.  Global Strong Solution With BV Derivatives to Singular Solid-on-Solid model With Exponential Nonlinearity   Journal of Differential Equations, 267(7), 4429-4447, (2019). 

11.  Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects  with J.-G. Liu, J. Lu, J.L. Marzuola,  Nonlinearity, 33, 3816-3845 (2020). 

12.  Long time behavior of dynamic solution to Peierls--Nabarro dislocation model  with J.-G. Liu,   Methods and Applications of Analysis, 27, 161-198, (2020).  

13.  A note on parametric Bayesian inference via gradient flows,  with J.-G. Liu, Annals of Mathematical Sciences and Applications, 261-282 (2020).  

14. Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation with Y. Gao and J.-G. Liu,   Quart. Appl. Math. 79, 55-102 (2021). 

15.  Mathematical validation of the Peierls--Nabarro model for edge dislocations  with J.-G. Liu, T. Lao and Y. Xiang, Discrete Contin. Dyn. Syst. Ser. B., 22, (2020).  

16.  Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface  with J.-G. Liu, to appear in Interfaces and Free Boundaries, (2021).  

17. Existence and uniqueness of bounded stable solutions to Peierls-Nabarro model for curved dislocation with H. Dong,   Calculus Var. Partial Differ. Equ., 60:62, (2021). 

18. Inbetweening auto-animation via Fokker-Planck dynamics and thresholding,  with G. Jin and J.-G. Liu,  to appear in Inverse Problems and Imaging, (2021). Video for facial aging process.  

19. Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates,  with A.E. Katsevich, J.-G. Liu, J. Lu, and J.L. Marzuola,  to appear in Pure and Applied Analysis, (2021). 

20. Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects,  with X.Y. Lu and C. Wang,  to appear in Adv. Calc. Var.(2021). 

21. Projection method for droplet dynamics on groove-textured surface with merging and splitting,  with J.-G. Liu,  submitted. 

22. Data-driven efficient solvers and predictions of conformational transitions for Langevin dynamics on manifold in high dimensions,  with J.-G. Liu and N. Wu  submitted. 

23. Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions,  with J.-G. Liu and Zibu Liu,  submitted. 

24.  Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver,  with T. Li, X. Li and J.-G. Liu,  submitted. 

25.  Surfactant-dependent contact line dynamics and droplet adhesion on textured substrates: derivations and computations,  with J.-G. Liu,  submitted. 

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