Research Areas:Control Theory of Partial Differential Equations, in particular on stabilization, 

            controllability and synchronization of hyperbolic systems

  0531-88369817

  hul@sdu.edu.cn

2006.9–2010.6, B.S., School of Mathematical Sciences, Ocean University of China, China

2010.9–2015.6, Ph. D, School of Mathematical Sciences, Fudan University, China

2013.9–2015.6, Ph. D, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (now known as Sorbonne Université), France

2015.11–Present, School of Mathematics, Shandong University, China

National Science Fund for Excellent Young Scholar

[1] Long Hu and Guillaume Olive. The minimal control time for the exact controllability by internal controls of 1D linear hyperbolic balance laws. 2024, preprint, submitted. https://arxiv.org/abs/2403.20113.

[2] Xiaomin Xue, Juanjuan Xu, Huanshui Zhang and Long Hu. LQ Optimal Control of First-Order Hyperbolic PDE Systems with Final State Constraints. 2024, preprint, submitted. https://arxiv.org/abs/2402.04537.

[3] Long Hu and Qing Zhang. Boundary stabilization of linear hyperbolic integro-differential equation with time-dependent coefficients. 2024, preprint, submitted.

[4] Long Hu and G. Olive. Minimal null control time of some 1D hyperbolic balance laws with constant coefficients and properties of related kernel equations. 2023, preprint, submitted. https://hal.science/hal-04318642.

[5] Long Hu and Guillaume Olive. Equivalent one-dimensional first-order linear hyperbolic systems and range of the minimal null control time with respect to the internal coupling matrix. J. Differential Equations 336 (2022), 654–707.

[6] Long Hu and Guillaume Olive. Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2 × 2 linear hyperbolic systems. ESAIM Control Optim. Calc. Var. 27 (2021), Paper No. 96, 18 pp.  

[7] Long Hu and Guillaume Olive. Minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls. J. Math. Pures Appl. (9) 148 (2021), 24–74.  

[8] Jean-Michel Coron, Long Hu, Guillaume Olive and Peipei Shang. Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. J. Differential Equations 271 (2021), 1109–1170.  

[9] Long Hu, Rafael Vazquez, Florent Di Meglio and Miroslav Krstic. Boundary exponential stabilization of 1-dimensional inhomogeneous quasi-linear hyperbolic systems. SIAM J. Control Optim. 57 (2019), no. 2, 963–998.  

[10] Florent Di Meglio, Federico Bribiesca Argomedo,  Long Hu and Miroslav Krstic. Stabilization of coupled linear heterodirectional hyperbolic PDE-ODE systems. Automatica J. IFAC 87 (2018), 281–289.  

[11] Jean-Michel Coron, Long Hu and Guillaume Olive. Finite-time boundary stabilization of general linear hyperbolic balance laws via Fredholm backstepping transformation. Automatica J. IFAC 84 (2017), 95–100.  

[12] Long Hu, Florent Di Meglio, Rafael Vazquez and Miroslav Krstic. Control of homodirectional and general heterodirectional linear coupled hyperbolic PDEs. IEEE Trans. Automat. Control 61 (2016), no. 11, 3301–3314.  

[13] Long Hu, Tatsien Li and Peng Qu. Exact boundary synchronization for a coupled system of 1-D quasilinear wave equations. ESAIM Control Optim. Calc. Var. 22 (2016), no. 4, 1163–1183.  

[14] Jean-Michel Coron, Long Hu and Guillaume Olive. Stabilization and controllability of first-order integro-differential hyperbolic equations. J. Funct. Anal. 271 (2016), no. 12, 3554–3587.

[15] Long Hu and Zhiqiang Wang. On boundary control of a hyperbolic system with a vanishing characteristic speed. ESAIM Control Optim. Calc. Var. 22 (2016), no. 1, 134–147.  

[16] Long Hu. Sharp time estimates for exact boundary controllability of quasilinear hyperbolic systems. SIAM J. Control Optim. 53 (2015), no. 6, 3383–3410.

[17] Long Hu and Florent Di Meglio. Finite-time backstepping boundary stabilization of 3×3 hyperbolic systems, in Proceedings of the European Control Conference (ECC) (July 2015) 67–72.

[18] Tatsien Li, Bopeng Rao and Long Hu. Exact boundary synchronization for a coupled system of 1-D wave equations. ESAIM Control Optim. Calc. Var. 20 (2014), no. 2, 339–361.  

[19] Long Hu, Tatsien Li and Bopeng Rao. Exact boundary synchronization for a coupled system of 1-D wave equations with coupled boundary conditions of dissipative type. Commun. Pure Appl. Anal. 13 (2014), no. 2, 881–901.  

[20] Long Hu, Fanqiong Ji and Ke Wang. Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations. Chinese Ann. Math. Ser. B 34 (2013), no. 4, 479–490.  

·Control Theory of Hyperbolic Partial Differential Equations, National Science Fund for Excellent Young Scholar, 2022-2024, PI

·Optimal time for the boundary controllability and stabilization of coupled hyperbolic systems, National Natural Science Foundation of China (General Program), 2021-2024, PI.

·Controllability of Hyperbolic Systems with a reduced number of controls, Key R&D Program of Shandong Province, 2019-2021, PI.

·Boundary synchronization for 1-D nonlinear coupled hyperbolic systems, National Natural Science Foundation of China (Youth Program), 2017-2019, PI.

·The Young Elite Scientists Sponsorship Program by Shandong Province，Shandong Association for Science &Technology, 2018-2020, PI.

·The National Postdoctoral Program for Innovative Talents, Ministry of Human Resources and Social Security & National Postdoctoral Management Committee, 2016-2018, PI.