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Yu Wang 王宇

Assistant professor

About me

Welcome to my personal webpage. I am an Assistant Professor of Mathematics at Southwest Jiaotong University.

My research primarily focuses on control theory for stochastic partial differential equations (SPDEs) and inverse problems within this context. These areas of mathematics are essential for understanding systems affected by random disturbances, which have significant implications in various scientific and engineering applications.

One of my interests is the controllability of SPDEs. Controllability concerns the ability to steer a system from any initial state to a desired final state within a finite time, employing suitable controls. The inherent randomness in SPDEs renders this a challenging task, as numerous tools and techniques for deterministic systems prove ineffectual.

My work in this domain concentrates on null controllability concerning linear fourth order SPDEs. Through the utilization of duality arguments, I have reduced null controllability to the observability of backward fourth order SPDEs. The desired observability estimate was established by constructing a global Carleman estimate.

Click to expand papers
  • Q. Lü, Y. Wang, Null Controllability for Fourth Order Stochastic Parabolic Equations, SIAM J. Control Optim., 60 (2022) 1563–1590. [Article] [ArXiv]
  • Q. Lü, Y. Wang, Exact Controllability for a Refined Stochastic Plate Equation, Chinese Ann. Math. Ser. B., Accepted. [ArXiv]
  • Y. Wang, Null controllability for stochastic coupled systems of fourth order parabolic equations, J. Math. Anal. Appl., 538 (2024), 128426. [Article] [ArXiv]

I also focus on semi-discrete systems as they approximate continuous systems. In this context, I have studied the null controllability of certain semi-discrete SPDEs, introducing new, refined semi-discrete Carleman estimates.

Click to expand papers
  • Y. Wang, Q. Zhao, Null controllability for semi-discrete stochastic semilinear parabolic equations, Submitted. [ArXiv]
  • Y. Wang, Q. Zhao, Null controllability for stochastic fourth order semi-discrete parabolic equations, Submitted. [ArXiv]

Another focal point of my research is inverse problems in SPDEs. In general, inverse problems aim to ascertain the latent parameters of a system from observed data with respect to a mathematical model of the system.

In this domain, I have explored ill-posed Cauchy problems for stochastic parabolic equations. My contributions include deriving the conditional stability and convergence rate of the Tikhonov regularization method for these ill-posed Cauchy problems.

Click to expand papers
  • F. Dou, P. Lü, Y. Wang, Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation, Inverse Problem, vol. 40, no. 11 (2024), p. 115005. [Article] [ArXiv]
  • Q. Lü, Y. Wang, Inverse problems for stochastic partial differential equations, Submitted. [ArXiv]

Working experience

Education

  • 09.2017 - 06.2023 Ph.D. in Mathematics, Sichuan University (Supervisor: Professor Qi Lü (吕琦)).
  • 09.2013 - 06.2017 B.Sc. in Mathematics, Sichuan University.

Publications

Articles

  1. F. Dou, P. Lü, Y. Wang, Stability and regularization for ill-posed Cauchy problem of a stochastic parabolic differential equation, Inverse Problem, vol. 40, no. 11 (2024), p. 115005. [Article] [ArXiv]
  2. Y. Wang, Null controllability for stochastic coupled systems of fourth order parabolic equations, J. Math. Anal. Appl., 538 (2024), 128426. [Article] [ArXiv]
  3. Q. Lü, Y. Wang, Null Controllability for Fourth Order Stochastic Parabolic Equations, SIAM J. Control Optim., 60 (2022) 1563–1590. [Article] [ArXiv]

Preprints

  1. Y. Wang, Q. Zhao, Null controllability for semi-discrete stochastic semilinear parabolic equations, Submitted. [ArXiv]
  2. Q. Lü, Y. Wang, Inverse problems for stochastic partial differential equations, Submitted. [ArXiv]
  3. Y. Wang, Q. Zhao, Null controllability for stochastic fourth order semi-discrete parabolic equations, Submitted. [ArXiv]
  4. Q. Lü, Y. Wang, Exact Controllability for a Refined Stochastic Plate Equation, Chinese Ann. Math. Ser. B., Accepted. [ArXiv]

Grants

  1. Controllability of fourth order semilinear stochastic partial differential equations, 2025-2027, RMB 300K. National Natural Science Foundation of China (No. 12401589).

    国家自然科学基金青年科学基金项目 (No. 12401589), 四阶半线性随机偏微分方程的能控性, 2025-2027, 30万元.

  2. Controllability of a fourth-order coupled stochastic parabolic system, 2024-2026, RMB 100K. Fundamental Research Funds for the Central Universities (No. 2682024CX013).

    中央高校基本科研业务费 (No. 2682024CX013), 耦合四阶随机抛物型系统的能控性, 2024-2026, 10万元.

Peer review

  • SIAM Journal on Control and Optimization
  • ESAIM: Control, Optimisation and Calculus of Variations
  • Journal of Systems Science and Complexity
  • Mathematical Control and Related Fields
  • Science China Mathematics
  • Applied Mathematics & Optimization
  • Journal of Mathematical Analysis and Applications

Courses

  • 2025Neural Networks and Deep Learning (神经网络与深度学习)
  • 2024Introduction to Major (专业导论)