个人简介

江苏江阴人。现任必威betway东盟体育教授。

研究兴趣

主要研究具有几何或物理背景的椭圆型偏微分方程，如Allen-Cahn方程、KP方程、Ginzburg-Landau方程等。

主讲课程

《复变函数论》，《数学分析》等。

学习经历

1998年9月-2002年7月，四川大学数学系，本科；

2002年9月-2007年7月，北京大学数学科学学院，硕博连读。

工作经历

2007年7月-2018年10月，华北电力大学（北京）数理学院，讲师、副教授；

2008年9月-2011年9月，智利大学数学中心，博士后；

2018年11月-2024年9月，中国科学技术大学数学科学学院，教授；

2020年1月-2021年12月，中国科学院学部工作局，处长助理、副处长；

2024年9月-至今，必威betway东盟体育，教授。

主要科研项目

主要有：

1. 国家自然科学基金面上项目，KP方程与Toda晶格相关问题的研究，2025，主持；

2. 国家自然科学基金面上项目，Gross-Pitaevskii方程及Ermakov系统相关问题的研究，2020，主持；

3. 国家自然科学基金青年项目，从Scherk曲面到Allen-Cahn方程的整体解，2012，主持；

4. 科技部国家重点研发计划（子课题），Monge-Ampere方程，Allen-Cahn方程及极小曲面，2022，参与；

5. 国家自然科学基金专项项目，几何非线性椭圆偏微分方程，2022，参与；

6. 科技部国家重点研发计划（子课题）， 非线性偏微分方程及应用，2020，参与。

主要学术成果

[1] Y. Liu, J. Wei, W. Yang, Lump type solutions: Bäcklund transformation and spectral properties, Physica D: Nonlinear Phenomena 470 (2024) 134394.

[2] W. Liang, Y. Liu, J. Yang, From Liouville equation to lump solutions of the 2+1 Toda lattice, Journal of Differential Equations 411 (2024) 478–505.

[3] Y. Liu, Y. Zhang, Fence of saddle solutions of the Allen–Cahn equation in the plane, Proceedings of the Royal Society of Edinburgh: Section A Mathematics (2024) 1–42.

[4] Y. Liu, J. Wei, W. Yang, Uniqueness of lump solution to the KP‐I equation, Proceedings of London Math Soc 129 (2024) e12619.

[5] L. Cui, Y. Liu, C. Wang, J. Wang, W. Yang, The Einstein-scalar field Lichnerowicz equations on graphs, Calc. Var. 63 (2024) 138.

[6] Y. Liu, K. Wang, J. Wei, K. Wu, On Dancer’s conjecture for stable solutions with sign-changing nonlinearity, Proc. Amer. Math. Soc. 152 (2024) 3485–3497.

[7] Liu, Yong; Ma, Xi-Nan; Wei, Juncheng; Wu, Wangzhe, Entire solutions of the magnetic Ginzburg-Landau equation in R^4, The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, accepted, https://doi.org/10.2422/2036-2145.202209_005

[8] Liu, Yong; Tian, Jing; Yong, Xuelin, On the even solutions of the Toda system: a degree argument approach, Commun. Pure Appl. Anal. 21 (2022), no. 6, 1895–1916.

[9] Liu, Yong; Wei, Juncheng, Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane, Rev. Mat. Iberoam. 38 (2022), no. 2, 355–432.

[10] Ao, Weiwei; Liu, Yong; Wei, Juncheng,  Clustered travelling vortex rings to the axisymmetric three-dimensional incompressible Euler flows, Phys. D 434 (2022), Paper No. 133258, 26 pp.

[11] Liu, Yong; Wang, Kelei; Wei, Juncheng; Wu, Ke,  Qualitative properties of stable solutions to some supercritical problems, Electron. Res. Arch. 30 (2022), no. 5, 1668–1690.

[12] Ao, Weiwei; Huang, Yehui; Liu, Yong; Wei, Juncheng, Generalized Adler-Moser polynomials and multiple vortex rings for the Gross-Pitaevskii equation, SIAM J. Math. Anal. 53 (2021), no. 6, 6959–6992.

[13] Liu, Yong; Wang, Kelei; Wei, Juncheng, On smooth solutions to one phase-free boundary problem in R^n, Int. Math. Res. Not. IMRN (2021), no. 20, 15682–15732.

[14] Hamel, François; Liu, Yong; Sicbaldi, Pieralberto; Wang, Kelei; Wei, Juncheng, Half-space theorems for the Allen-Cahn equation and related problems, J. Reine Angew. Math. 770 (2021), 113–133.

[15] Liu, Yong; Wei, Juncheng, Multivortex traveling waves for the Gross-Pitaevskii equation and the Adler-Moser polynomials, SIAM J. Math. Anal. 52 (2020), no. 4, 3546–3579.

[16] Chen, Guoyuan; Liu, Yong; Wei, Juncheng, Nondegeneracy of harmonic maps from R^2 to S^2, Discrete Contin. Dyn. Syst. 40 (2020), no. 6, 3215–3233.

[17] Yong, Xuelin; Li, Xiaoyu; Huang, Yehui; Ma, Wen-Xiu; Liu, Yong, Rational solutions and lump solutions to the (3+1)-dimensional Mel'nikov equation, Modern Phys. Lett. B 34 (2020), no. 3, 2050033, 14 pp.

[18] Liu, Yong; Wei, Juncheng, Nondegeneracy, Morse index and orbital stability of the KP-I lump solution, Arch. Ration. Mech. Anal. 234 (2019), no. 3, 1335–1389.

[19] Liu, Yong; Wei, Juncheng, On the Helmholtz equation and Dancer's-type entire solutions for nonlinear elliptic equations, Proc. Amer. Math. Soc. 147 (2019), no. 3, 1135–1148..

[20] Liu, Yong; Wei, Juncheng, Nondegeneracy of the traveling lump solution to the 2+1 Toda lattice, J. Math. Phys. 59 (2018), no. 10, 101501, 26 pp.

[21] Liu, Yong; Wang, Kelei; Wei, Juncheng, On a free boundary problem and minimal surfaces, Ann. Inst. H. Poincaré C Anal. Non Linéaire 35 (2018), no. 4, 993–1017.

[22] Yong, Xuelin; Ma, Wen-Xiu; Huang, Yehui; Liu, Yong, Lump solutions to the Kadomtsev-Petviashvili I equation with a self-consistent source, Comput. Math. Appl. 75 (2018), no. 9, 3414–3419.

[23]  Liu, Yong; Wang, Kelei; Wei, Juncheng, Global minimizers of the Allen-Cahn equation in dimension n≥8, J. Math. Pures Appl. (9) 108 (2017), no. 6, 818–840.

[24] Gui, Changfeng; Liu, Yong; Wei, Juncheng, Two-end solutions to the Allen-Cahn equation in R^3, Adv. Math. 320 (2017), 926–992.

[25] Gui, Changfeng; Liu, Yong; Wei, Juncheng,  On variational characterization of four-end solutions of the Allen-Cahn equation in the plane, J. Funct. Anal. 271 (2016), no. 10, 2673–2700.

[26] Kowalczyk, Michał; Liu, Yong; Pacard, Frank; Wei, Juncheng, End-to-end construction for the Allen-Cahn equation in the plane, Calc. Var. Partial Differential Equations 52 (2015), no. 1-2, 281–302.

[27] Kowalczyk, Michał; Liu, Yong; Wei, Juncheng, Singly periodic solutions of the Allen-Cahn equation and the Toda lattice, Comm. Partial Differential Equations 40 (2015), no. 2, 329–356.

[28] Kowalczyk, Michał; Liu, Yong; Pacard, Frank, Multiple end solutions to the Allen-Cahn equation in R^2, Éditions de l'École Polytechnique, Palaiseau, 2014, Exp. No. X, 19 pp. ISBN: 978-2-7302-1633-3.

[29] Kowalczyk, Michał; Liu, Yong; Pacard, Frank, The classification of four-end solutions to the Allen-Cahn equation on the plane, Anal. PDE 6 (2013), no. 7, 1675–1718.

[30] Kowalczyk, Michał; Liu, Yong; Pacard, Frank, Towards classification of multiple-end solutions to the Allen-Cahn equation in R^2, Netw. Heterog. Media 7 (2012), no. 4, 837–855.

[31] Kowalczyk, Michał; Liu, Yong; Pacard, Frank, The space of 4-ended solutions to the Allen-Cahn equation in the plane, Ann. Inst. H. Poincaré C Anal. Non Linéaire 29 (2012), no. 5, 761–781.

[32] Kowalczyk, Michał; Liu, Yong, Nondegeneracy of the saddle solution of the Allen-Cahn equation, Proc. Amer. Math. Soc. 139 (2011), no. 12, 4319–4329.

[33] Liu, Yong, Even solutions of the Toda system with prescribed asymptotic behavior, Commun. Pure Appl. Anal. 10 (2011), no. 6, 1779–1790.

[34] Liu, Yong, Morse homology of super-quadratic Hamiltonian systems on R^{2n},J. Math. Anal. Appl. 344 (2008), no. 1, 384–407.

[35] Liu, Yong; Jiang, Mei-Yue, Periodic bounce solutions of Hamiltonian systems in bounded domains, Adv. Nonlinear Stud. 7 (2007), no.4, 533–550.