Publication List

1. Preprints:

  1. Gao, Y., J. -G. Liu, O. Tse. “Optimal control formulation of transition path problems for Markov Jump Processes”, submitted.
  2. Gao, Y., N. K. Yip. “Homogenization of Wasserstein gradient flows”, submitted.
  3. Gao, Y., D. Qi. “Mean Field Games for Controlling Coherent Structures in Nonlinear Fluid Systems”, submitted.

2. Peer-reviewed Publications:

  1. Gao, Y., W. Li, and J. -G. Liu. “Master equations for finite state mean field games with nonlinear activations”, to appear in Discrete and Continuous Dynamical Systems Series B. (2024). Full text:
  2. Gao, Y., and J.M. Scott. “Existence and uniqueness of solutions to the Peierls-Nabarro model in anisotropic media”, Nonlinearity, 37: 1-30. (2024). Full text:
  3. Liu, C., Y. Gao, and X. X. Zhang. “Structure preserving schemes for Fokker-Planck equations of irreversible processes”, Journal of Scientific Computing, 98(4). (2024). Full text:
  4. Gao, Y., and J. -G. Liu. “A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures”, SIAM Journal on Mathematical Analysis, 55(6): 6457-6495. (2023). Full text:
  5. Gao, Y., and Y. F. Zhou. “Hamilton Dynamics in Chemical Reactions: the Maupertuis Principle, Transition Paths and Energy Landscape”, 2(3): 245-288. (2023). Full text:
  6. Gao, Y. and J. -G. Liu. “Large deviation principle and thermodynamic limit of chemical master equation via nonlinear semigroup”, Multiscale Modeling and Simulation. 21(4): 1534-1569. (2023). Full text:
  7. Gao, Y., and J. -G. Liu. “Random walk approximation for irreversible drift-diffusion process on manifold: ergodicity, unconditional stability and convergence”, Communications in Computational Physics. 34(1): 132-172. (2023) Full text:
  8. Gao, Y. and J.-M. Roquejoffre. “Asymptotic stability for diffusion with dynamic boundary reaction from Ginzburg-Landau energy”, SIAM Mathematical Analysis. 55(2): 1246-1263. (2023) Full text:
  9. Gao, Y., T. Li, X. Li, and J. -G. Liu. “Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver”, Multiscale Modeling and Simulation. 21(1): 1-33. (2023) Full text:
  10. Gao, Y., J. -G. Liu, and N. Wu. “Data-driven Efficient Solvers for Langevin Dynamics on Manifold in High Dimensions”, Applied and Computational Harmonic Analysis. 62: 261-309. (2023) Full text:
  11. Gao, Y., and J. -G. Liu. “Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint”, Journal of Statistical Physics. 189(22). (2022). Full text:
  12. Gao, Y., and J. -G. Liu. “Projection method for droplet dynamics on groove-textured surface with merging and splitting”, SIAM Journal on Scientific Computing. 44(2): B310–B338. (2022). Full text:
  13. Gao, Y., A.E. Katsevich, J.-G. Liu, J. Lu, and J.L. Marzuola. “Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates”, Pure and Applied Analysis. 3(4): 595-612. (2022). Full text:
  14. Gao, Y., and J. -G. Liu. “Surfactant-dependent contact line dynamics and droplet adhesion on textured substrates: derivations and computations”, Physica D: Nonlinear Phenomena. 428: 133067. (2021). Full text:
  15. Gao, Y., J. -G. Liu, and Z. Liu. “Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions”, Nonlinearity. 34(11): 7778–7828. (2021). Full text:
  16. Gao, Y., G. Jin, and J. -G. Liu. “Inbetweening auto-animation via Fokker-Planck dynamics and thresholding”. Inverse Problems and Imaging. 15(5): 843-864. (2021). Full text: Video for facial aging process:
  17. Gao, Y., and J. -G. Liu. “Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface”. Interfaces and Free Boundaries. 23(1): 103–158. (2021). Full text:
  18. Gao, Y., X. Y. Lu, and C. Wang. “Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects”. Advances in Calculus of Variations. 000010151520200114. (2021). Full text:
  19. Dong, H., and Y. Gao. “Existence and uniqueness of bounded stable solutions to the Peierls–Nabarro model for curved dislocations”. Calculus of Variations and Partial Differential Equations. 60(62). (2021). Full text:
  20. Gao. Y., and J. -G. Liu. “A note on parametric Bayesian inference via gradient flows.” Annals of Mathematical Sciences and Applications. 5(2): 261–282. (2020). Full text:
  21. Gao, Y., J. -G. Liu, T. Luo, and Y. Xiang. “Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space”. Discrete and Continuous Dynamical Systems Series B. 26(6): 3177-3207. (2020).
  22. Gao, Y., J. -G. Liu, J. Lu and J. L. Marzuola. “Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects”. Nonlinearity. 33(8): 3816-3845. (2020). Full text:
  23. Gao, Y., Y. Gao, and J. -G. Liu. “Large Time Behavior, bi-Hamiltonian Structure, and Kinetic Formulation for a Complex Burgers Equation”. Quarterly of Applied Mathematics. 79(1): 55-102. (2020). Full text:
  24. Gao, Y., and J. -G. Liu. “Long time behavior of dynamic solution to Peierls–Nabarro dislocation model”. Methods and Applications of Analysis. 27(2): 161–198. (2020) Full text:
  25. Gao, Y.. “Global strong solution with BV derivatives to singular solid-on-solid model with exponential nonlinearity”. Journal of Differential Equations. 267(7): 4429–4447. (2019). Full text:
  26. Gao, Y., J. -G. Liu, and X. Y. Lu. “Gradient flow approach to an exponential thin film equation: Global existence and latent singularity”. Esaim Control, Optimisation and Calculus of Variations. 25(49). (2019). Full text:
  27. Gao, Y., H. Ji, J. -G. Liu, and T. P. Witelski. “A vicinal surface model for epitaxial growth with logarithmic free energy”. Discrete and Continuous Dynamical Systems Series B. 23(10): 4433–4453. (2018). Full text:
  28. Jin, G., H. Pan, Q. Zhang, X. Lv, W. Zhao, and Y. Gao. “Determination of Harmonic Parameters with Temporal Variations: An Enhanced Harmonic Analysis Algorithm and Application to Internal Tidal Currents in the South China Sea.” Journal of Atmospheric and Oceanic Technology. 35(7): 1375-1398. (2018). Full text:
  29. Gao, Y., J. -G. Liu, X. Y. Lu, and X. Xu. “Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface”. Calculus of Variations and Partial Differential Equations. 57(2): 55. (2018). Full text:
  30. Gao, Y., J. Liang, and T. J. Xiao. “A new method to obtain uniform decay rates for multidimensional wave equations with nonlinear acoustic boundary conditions”. Siam Journal on Control and Optimization. 56(2): 1303–1320. (2018). Full text:
  31. Gao, Y., J. Liang, and T. J. Xiao. “Observability inequality and decay rate for wave equations with nonlinear boundary conditions”. Electronic Journal of Differential Equations. 2017(161): 1-12. (2017). Full text:
  32. Gao, Y., H. Ji, J. -G. Liu, and T. P. Witelski. “Global existence of solutions to a tear film model with locally elevated evaporation rates”. Physica D: Nonlinear Phenomena. 350: 13–25. (2017). Full text:
  33. Gao, Y., J. -G. Liu, and J. Lu. “Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces”. Journal of Nonlinear Science. 27(3): 873–926. (2017). Full text:
  34. Gao, Y., J. -G. Liu, and J. Lu. “Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime”. Siam Journal on Mathematical Analysis. 49(3): 1705–1731. (2017). Full text: