Applied mathematics
Haitian Yang 杨海天
I am currently a postdoctoral researcher at IRMAR, Université de Rennes, France, in the project of Prof. L. Miguel Rodrigues. I received my Ph.D. in Applied Mathematics from Tsinghua University in 2026, under the supervision of Prof. Wen-An Yong, and my bachelor’s degree in Mathematics and Economics from Tsinghua University in 2021.
Research
I work in applied mathematics, and my interest lies in using mathematics to understand systems arising in physics, engineering, economics and computing, and to control them. During my Ph.D., I extended J.-M. Coron’s boundary control theory for one-dimensional first-order hyperbolic systems to several space dimensions, covering boundary stabilization, boundary controllability and boundary optimal control. These results apply in particular to the Saint-Venant equations, which describe water flow in rivers and coastal seas.
Open ocean · deep water
Water-wave equations
Δφ = 0in −h < y < η∂tη = ∂yφ − ∂xη ∂xφon y = η∂tφ + ½|∇φ|2 + gη = 0on y = η
The water is as deep as the waves are long, or deeper, so dispersion acts in full. The flow is incompressible and irrotational, with a free surface.
Continental shelf · intermediate depth
Long waves with weak dispersion
ut + ux + uux − uxxt = 0(BBM)ut + ux + uux + uxxx = 0(KdV)ηt + ((1 + η)u)x = 0ut + ηx + uux − uxxt = 0(Boussinesq)
Waves are long and low compared with the depth, to a comparable degree, so nonlinearity balances dispersion and solitary waves form. BBM and KdV are one-way models; Boussinesq systems carry waves in both directions.
My workIn preparation: hyperbolic approximations of these dispersive equations.
Nearshore · shallow water
Shallow-water (Saint-Venant) equations
ht + (hu)x = 0ut + uux + ghx = φ(1D)ht + (hu)x + (hv)y = 0ut + uux + vuy + ghx = φ1vt + uvx + vvy + ghy = φ2(2D)
Waves are far longer than the water is deep, and no longer low compared with it: nonlinearity dominates and dispersion drops out, so wave fronts steepen into bores before breaking and running up the beach.
My workBoundary stabilization and optimal control of the Saint-Venant equations through sluice gates.
- Feedback boundary control … with relaxation · Automatica 2024
- Exponential turnpike in optimal boundary control · preprint 2026
Publications
2026
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[6]
Boundary stabilization of multi-dimensional first-order quasilinear hyperbolic systems
H. Yang
Preprint, arXiv:2610.13577
StabilizationPreprintarXiv
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[5]
Exponential turnpike in optimal boundary control of multi-dimensional first-order hyperbolic systems
H. Yang
Preprint, arXiv:2609.14601
Optimal controlPreprintarXiv
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[4]
Exact controllability for stochastic first-order multi-dimensional hyperbolic systems
Z. Li, Q. Lü, Y. Wang, H. Yang
SIAM Journal on Control and Optimization, accepted
ControllabilityJournalarXiv
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[3]
Numerical boundary control of multi-dimensional discrete-velocity kinetic models
H. Yang, W.-A. Yong
Systems & Control Letters 217 (2026), 106561
StabilizationJournalarXiv
2025
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[2]
Boundary control of multi-dimensional discrete-velocity kinetic models
H. Yang, W.-A. Yong
IEEE Transactions on Automatic Control (2025)
StabilizationJournalarXivIEEE Xplore
2024
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[1]
Feedback boundary control of multi-dimensional hyperbolic systems with relaxation
H. Yang, W.-A. Yong
Automatica 167 (2024), 111791
StabilizationJournalarXivScienceDirect
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Talks
- Recent Developments in Boundary Stabilization of the Two-dimensional Saint-Venant Equations
- Sep 2026ShanghaiTech University, Shanghai, ChinaManuel Rissel, Zhuo Xu
- Boundary Control of Multi-dimensional First-order Hyperbolic Systems
- Apr 9, 2026École des Ponts ParisTech, Paris, FranceAmaury Hayat
- Mar 24, 2026Bergische Universität Wuppertal, GermanyBirgit Jacob
- Feb 24, 2026FEMTO-ST, Besançon, FranceYann Le Gorrec, Yongxin Wu
- Feb 19, 2026IRMAR, Rennes, FranceL. Miguel Rodrigues
- Feb 17, 2026Institut de Mathématiques de Toulouse, FranceTimothée Crin-Barat
- Feb 4, 2026Chair of Applied Mathematics, Stuttgart, GermanyChristian Rohde
- Jan 14, 2026IGPM, Aachen, GermanyMichael Herty
- Nov 2025FAU DCN-AvH, Erlangen and Speinshart, GermanyEnrique Zuazua
Teaching
- Teaching assistant, Tsinghua University2021 – 2025 · Per course: 32 hours of exercise sessions, in addition to office hours and grading
- Fall 2021Calculus IOutstanding Teaching Assistant Award (inaugural, university-level)Ping Yan
- Spring 2022Partial Differential Equations IWen-An Yong
- Fall 2022Ordinary Differential EquationsSi-Qi Liu
- Spring 2023Analysis IIWenjia Jing
- Fall 2023Partial Differential Equations IIYang Lan
- Spring 2024Differential Geometry and Smooth ManifoldsOutstanding Teaching Assistant AwardHonghao Gao
- Fall 2024Complex AnalysisSebastian Heller
- Spring 2025TopologyHonghao Gao
Curriculum vitae
Positions
- CurrentPostdoctoral researcher, IRMAR, Université de Rennes, FranceIn the project of Prof. L. Miguel Rodrigues.
- 2025 – 2026Visiting Ph.D. student, FAU DCN-AvH, Erlangen, GermanyHosted by Prof. Enrique Zuazua, Nov 2025 – Apr 2026
Education
- 2021 – 2026Ph.D. in Applied Mathematics, Tsinghua UniversityAdvisor: Prof. Wen-An Yong.
- 2017 – 2021B.S. in Mathematics and Economics (double major), Tsinghua University