Publication List

1. Preprints:

  1. Gao, Y., A. Stephan. “Fast-slow chemical reactions: convergence of Hamilton-Jacobi equation and variational representation”, submitted. https://arxiv.org/abs/2412.14411v1
  2. Gao, Y., Q. J. Lang, F. Lu. “Self-test loss functions for learning weak-form operators and gradient flows”, submitted. https://arxiv.org/abs/2412.03506
  3. Gao, Y., W. Li, J. -G. Liu. “Fluctuations in Wasserstein dynamics on Graphs”, submitted. https://arxiv.org/abs/2408.08505
  4. Gao, Y., J. -G. Liu, O. Tse. “Optimal control formulation of transition path problems for Markov Jump Processes”, submitted. https://doi.org/10.48550/arXiv.2311.07795
  5. Gao, Y., N. K. Yip. “Homogenization of Wasserstein gradient flows”, submitted. https://doi.org/10.48550/arXiv.2312.01584
  6. Gao, Y., D. Qi. “Mean Field Games for Controlling Coherent Structures in Nonlinear Fluid Systems”, submitted. https://doi.org/10.48550/arXiv.2401.10356

2. Peer-reviewed Publications:

  1. Gao, Y., J. -G. Liu, Z. Liu. “Some properties on the reversibility and the linear response theory of Langevin dynamics”, Acta Applicandae Mathematicae, (2024) 194:12. https://doi.org/10.1007/s10440-024-00702-w Full text:
  2. Gao, Y., W. Li, and J. -G. Liu. “Master equations for finite state mean field games with nonlinear activations”, Discrete and Continuous Dynamical Systems Series B, 29(7): 2837-2879. (2024). https://doi.org/10.3934/dcdsb.2023204 Full text:
  3. Gao, Y., and J.M. Scott. “Existence and uniqueness of solutions to the Peierls-Nabarro model in anisotropic media”, Nonlinearity, 37: 1-30. (2024). https://doi.org/10.1088/1361-6544/ad1763 Full text:
  4. 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). https://doi.org/10.1007/s10915-023-02378-0 Full text:
  5. 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). https://doi.org/10.1137/22M1519717 Full text:
  6. Gao, Y., and Y. F. Zhou. “Hamilton Dynamics in Chemical Reactions: the Maupertuis Principle, Transition Paths and Energy Landscape”, Communications in Mathematical Analysis and Applications, 2(3): 245-288. (2023). https://doi.org/10.4208/cmaa.2023-0003 Full text:
  7. 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). https://doi.org/10.1137/22M1505633 Full text:
  8. 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) https://doi.org/10.4208/cicp.OA-2023-0021 Full text:
  9. 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) https://doi.org/10.1137/22M1469791 Full text:
  10. 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) https://epubs.siam.org/doi/10.1137/21M1437883 Full text:
  11. 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) https://doi.org/10.1016/j.acha.2022.09.003 Full text:
  12. 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). https://link.springer.com/article/10.1007/s10955-022-02985-5 Full text:
  13. 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). https://epubs.siam.org/doi/10.1137/20M1338563 Full text:
  14. 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). https://doi.org/10.2140/paa.2021.3.595 Full text:
  15. 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). https://doi.org/10.1016/j.physd.2021.133067 Full text:
  16. 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). https://iopscience.iop.org/article/10.1088/1361-6544/ac24e3 Full text:
  17. 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). http://dx.doi.org/10.3934/ipi.2021016 Full text: Video for facial aging process:
  18. 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). https://doi.org/10.4171/ifb/451 Full text:
  19. 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). https://doi.org/10.1515/acv-2020-0114 Full text:
  20. 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). https://doi.org/10.1007/s00526-021-01939-1 Full text:
  21. 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). https://dx.doi.org/10.4310/AMSA.2020.v5.n2.a3 Full text:
  22. 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). http://dx.doi.org/10.3934/dcdsb.2020224
  23. 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). https://doi.org/10.1088/1361-6544/ab853d Full text:
  24. 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). https://doi.org/10.1090/QAM/1573 Full text:
  25. 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) https://doi.org/10.4310/maa.2020.v27.n2.a4 Full text:
  26. 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). https://doi.org/10.1016/j.jde.2019.05.011 Full text:
  27. 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). https://doi.org/10.1051/cocv/2018037 Full text:
  28. 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). https://doi.org/10.3934/dcdsb.2018170 Full text:
  29. 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). https://doi.org/10.1175/JTECH-D-16-0239.1 Full text:
  30. 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). https://doi.org/10.1007/s00526-018-1326-x Full text:
  31. 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). https://doi.org/10.1137/16M107863X Full text:
  32. 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:
  33. 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). https://doi.org/10.1016/j.physd.2017.03.005 Full text:
  34. 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). https://doi.org/10.1007/s00332-016-9354-1 Full text:
  35. 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). https://doi.org/10.1137/16M1094543 Full text: