非线性扩散方程 、 微分方程数值解 、 最优控制。

1.国家自然科学基金(青年基金)： 高阶非线性发展方程的整体吸引子与数值解法 (批准号：11401258)，22万，2015年1月至2017年12月，主持，在研。

2.江苏省自然科学基金(青年基金)：非线性高阶发展方程解的长时间行为及其最优控制(批准号：Bk0140130)，20万，2014年7月至2017年6月，主持，在研 。

3. 中央高校自主科研青年基金：高阶非线性发展方程的数值解法(批准号： JUSRP 11407) ， 8 万， 201 4年1月至2015年12月， 主持 ，在研。

4. 企业横向：新型耐温粘胶剂的市场调查与分析( 1144320000134910 )，6万，2013年11月至2015年11月，主持，在研。

5.国家自然科学基金(青年基金)： 多辛保结构变分数值方法及非标准有限差分方法在其上的应用 (批准号： 11401259 )，22万，2015年1月至2017年12月，参与，在研。

主要论著

[ 1 ] , X. Zhao and C. Liu, Optimal control problem for viscous Cahn–Hilliard equation , Nonlinear Analysis: Theory, Methods & Applications 74 (17) (2011) , 6348-6357 . [SCI, WOS:000293784500047 ]

[ 2 ] , X. Zhao, B. Liu and N. Duan, Existence of global attractor for the Trojan Y Chromosome model , Electronic Journal of Qualitative Theory of Differential Equations , 2012,No 36, 1-16. [SCI, WOS:000304408400001 ]

[ 3 ] , X. Zhao and C. Liu, Global attractor for a nonlinear model with periodic boundary value condition , Portugaliae Mathematica 69 ( 2012 ), 221-231 . [SCI, WOS:000311255800004 ]

[ 4 ] , X. Zhao and B. Liu, The existence of global attractor for convective Cahn-Hilliard equation , J. Korean Math. Soc ., 49 (2 012 ), 359-378 . [SCI, WOS:000301321600009 ]

[ 5 ] , X. Zhao, B. Liu and N. Duan, Time-periodic solution for a fourth-order parabolic equation describing crystal surface growth , Electronic Journal of Qualitative Theory of Differential Equations , 2013, No. 7, 1-15. [SCI, WOS: 000313178600001 ]

[ 6 ] , X. Zhao and C. Liu, The existence of global attractor for a fourth-order parabolic equation , Applicable Analysis , 92 (1) (2013) , 44-59 . [SCI, WOS: 000313032000004 ]

[ 7 ] , X. Zhao, B. Liu, P. Zhang, W. Zhang and F. Liu, Fourier spectral method for the modified Swift-Hohenberg equation , Advance in Difference Equations, 2013: 2013, 156. [SCI, WOS: 000321587000001 ]

[ 8 ] , X. Zhao and B. Liu, Global attractor for coupled two-compartment Gray-Scott equations , Bull. Korean Math. Soc., 50(2013),143-159. [SCI, WOS: 000324077000013 ]

[ 9 ] , X. Zhao, M. Zhang and C. Liu, Some properties of solutions for a fourth-order parabolic equation , Mathematical Methods in the Applied Sciences 36 (2 013 ), 169-181 . [SCI, WOS: 000312940500004 ]

[ 10 ] , X. Zhao and C. Liu, Optimal control of the convective Cahn–Hilliard equation , Applicable Analysis 92 ( 2013 ), 1028-1045 . [SCI, WOS:000315584900008 ]

[ 11 ] , X. Zhao and C. Liu, Optimal control of a fourth-order parabolic equation modeling epitaxial thin film growth. , Bulletin of the Belgian Mathematical Society-Simon Stevin 20 ( 2013), 547-557. [SCI, WOS:000325667500012 ]

[ 12 ] , X. Zhao, N. Duan and B. Liu, Optimal control problem of a generalized Ginzburg-Landau model equation in population problems , Mathematical Methods in the Applied Sciences 37 ( 2014 ), 435-446 . [SCI, WOS: 000329559200013 ]

[ 13 ] , X. Zhao, F. Liu and B. Liu, Finite element method for a nonlinear differential equation describing crystal surface growth , Mathematical Modeling and Analysis , 19(2014), 155-168. [SCI, WOS:000336036900002 ]

[ 14 ] , X. Zhao and C. Liu, Optimal control for the convective Cahn-Hilliard equation in 2D case, Applied Mathematics & Optimization , 70(2014), 61-82. [SCI, WOS:000339107200003 ]

[ 15 ] , X. Zhao and C. Liu, Time-periodic solution of a 2D fourth-order nonlinear parabolic equation , Proc. Indian Acad. Sci. (Math. Sci.) , 124(3)(2014), 349-364. [SCI, WOS:00034216 9600007 ]

[ 16 ] , X. Zhao, B. Liu and P. Zhang, The Fourier spectral approximation for Kolmogorov - Spiegel - Sivashinsky equation , Miskolc Mathematical Notes , 15(2014), 781-799. [SCI, WOS:000348602900046 ]

[ 17 ] , X. Zhao, A sixth-order parabolic equation describing continuum evolution of film free surface , Electron. J. Diff. Equ., Vol. 2014 (2014), No. 223, pp. 1-13. [SCI]

[ 18 ] , X. Zhao and C. Liu, On the existence of global attractor for 3D viscous Cahn-Hilliard equation, Acta. Appl. Math., Online, DOI: 10.1007/s10440-014-9963-3. [SCI]

[ 19 ] , X. Zhao, F. Liu and B. Liu, Finite difference discretization of a fourth-order parabolic equation describing crystal surface growth , Applicable Analysis, 2014 , Online, http://dx.doi.org/10.1080/00036811.2014.959440 . [SCI]

[ 20 ] , X. Zhao, Spectral approximations of attractors for convective Cahn-Hilliard equation in two dimensions , Bull. Korean Math. Soc., Accepted. [SCI]

[ 21 ] , X. Zhao, Z. Ning, Optimal control problem for the modi fi ed Swift-Hohenberg equation in 3D case , Mathematical Methods in the Applied Sciences , 2015, Online, DOI: 10.1002/mma.3442 . [SCI]