【高洪俊导师】招生“数学学院”研究生介绍
高洪俊
教授
硕，博士生导师
男
数学学院
数学
随机偏微分方程及其动力学
hjgao@seu.edu.cn
科研项目
2016年1月—2020年12月, 国家自然科学基金重点项目（1531006）, 随机动力系统的有效动力学及其刻画, 主持人, 直接经费230万.
2018年1月—2021年12月，国家自然科学基金，随机偏微分方程解的适定性与正则性及相关问题研究(11771123)，参与，48万.
2022年1月—2025年12月, 国家自然科学基金项目（12171084）， 非马尔可夫噪声驱动的随机偏微分方程的动力学， 主持人， 51万.
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研究成果
Selected Publications
1. H. Gao and J. E. M. Rivera, Global existence and decay for the semilinear thermoelastic contact problem, J. Differ. Eqns., Vol 186(2002), 52--68.
2. H. Gao and C. Bu, Dirichlet inhomogeneous boundary value problem for the n+1 complex Ginzburg-Landau equation, J. Differ. Eqns. 198 (2004), 176--195.
3. C. Sun, H. Gao, J. Duan and B. Schmalfuss, Rare Events in the Boussinesq System with Fluctuating Dynamical Boundary Conditions, J. Differ. Eqns., 248 (2010), no. 6, 1269–1296.
4. F. Guo, H. Gao and Y. Liu, Existence of permanent and breaking waves for the periodic Degasperis- Procesi equation with linear dispersion, Journal für reine und angewandte Mathematik, Volume 2011, Issue 657, Pages 199–223.
5. Y.Chen, H. Gao and B. Guo, Well posedness for stochastic Camassa-Holm equation, J. Differ. Eqns., 253( 2012), 2353–2379.
6. F. Guo, H. Gao and Y. Liu, On the wave-breaking phenomena for the two-component Dullin- Gottwald-Holm system, J. Lond. Math. Soc. (2), 86 (2012), no. 3, 810–834.
7. H. Gao, F. Liang and B. Guo, Stochastic wave equations with nonlinear damping and source terms, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 16 (2013), no. 2, 1350013, 29 pp.
8. Y. Han, F. Guo and H. Gao, On solitary waves and wave-breaking phenomena for a generalized two-component integrable Dullin-Gottwald-Holm system, J. Nonlinear Sci., 23 (2013), no. 4, 617–656.
9. H. Gao, M. J. Garrido-Atienza and B. Schmalfuss, Random attractors for stochastic evolution equations driven by fractional Brownian motion, SIAM J. Math. Anal., 46 (2014), no. 4, 2281–2309.
10. J. Fan, H. Gao and B. Guo, Uniqueness of Weak Solutions to the 3D Ginzburg– Landau Superconductivity Model, International Mathematics Research Notices, 2015(2015), 1239-12.
11. Y. Chen and H. Gao, The Cauchy problem for the Hartree equations under random influences, J. Differ. Eqns., 259(2015), 5192-5219.
12. L. Fan, H. Gao and Y. Liu, On the rotation-two-component Camassa-Holm system modelling the equatorial water waves, Advances in Mathematics, 291 (2016), 59–89.
13.Y. Chen and H. Gao, Well-posedness and Large Deviations of the Stochastic Modified Camassa-Holm Equation, Potential Analysis，45 (2016), 331–354.
14. L. Fan and H. Gao, Instability of equatorial edge waves in the background flow, Proceedings of the AMS，145 (2017), 765–778.
15. Y. Chen and H. Gao, Well-posedness and large deviations for a class of SPDEs with Levy noise, J. Differ. Eqns., 263(2017), 5216-5252.
16 .M. Chen, L. Fan, H. Gao ang Y. Liu, Breaking waves and solitary waves to the Rotation-Two- Component Camassa-Holm System, SIAM J. Math. Anal., 49(2017), 3573-3602.
17. Lin Lin and H. Gao, A Stochastic Generalized Ginzburg- Landau Equation Driven by Jump Noise, J. Theoretical Probab., 32(2019), 460–483.
18. G. Lv, H. Gao, J. Wei and J. Wu, BMO and Morrey-Campanato estimates for stochastic convolutions and Schauder estimates for stochastic parabolic equations, J. Differ. Eqns., 266(2019), 2666–2717.
19. H. Gao and H. Liu, Well-posedness and invariant measures for a class of stochastic 3D Navier-Stokes equations with damping driven by jump noise, J. Differ. Eqns., 267 (2019), 5938–5975.
20. J. Wei, J. Duan, H. Gao and G. Lv, Stochastic strong solution for stochastic transport equations, Stochastics and Partial Differential Equations: Analysis and Computations，9 (2021), no. 1, 105–141.
21. H. Gao, M. J. Garrido-Atienza, A. Gu, K. Lu and B. Schmalfuss, Rough path theory to approximate random dynamical systems, SIAM J. Appl. Dynamical Sys., 20 (2021), 997–1021.
22. B. Wang and H. Gao, Exponential stability of solutions to stochastic differential equations driven by G-Levy process, Appl. Math. Optim., 83 (2021), 1191–1218.
23. Y. Chen, J. Duan and H. Gao, Wave-breaking and moderate deviations of the stochastic Camassa-Holm with pure jump noise, Physica D, 424 (2021), Paper No. 132944, 12 pp.
24. H. Gao and Y. Shi, Averaging principle for a stochastic coupled fast-slow atmosphere-ocean model, J. Differ. Eqns., 298 (2021), 248–297.
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