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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.

You can find my CV here: CV (Google Drive).

My research primarily focuses on control theory for stochastic partial differential equations (SPDEs) and related inverse problems. These areas are crucial for understanding systems influenced by random disturbances, with broad applications in science and engineering.

One of my main interests is the controllability of SPDEs, which concerns the ability to steer a system from any initial state to a desired final state within a finite time using appropriate controls. The presence of randomness in SPDEs makes this a challenging problem, as many techniques for deterministic systems are not directly applicable.

My work in this area centers on null controllability for linear fourth order SPDEs. By employing duality arguments, I reduce the null controllability problem to establishing observability for backward fourth order SPDEs. The required observability estimate is obtained via 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 am also interested in semi-discrete systems, which serve as approximations of continuous systems. In this context, I have studied the null controllability of certain semi-discrete SPDEs and introduced 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. Broadly speaking, inverse problems seek to determine unknown parameters of a system from observed data, based on its mathematical model.

In this area, I have investigated ill-posed Cauchy problems and inverse source problems for stochastic partial differential equations. My work includes establishing conditional stability and convergence rates for the Tikhonov regularization method, as well as proposing efficient numerical algorithms for these problems.

Click to expand papers
  • Q. Lü, Y. Wang, An Inverse Source Problem for Semilinear Stochastic Hyperbolic Equations, Submitted. [ArXiv]
  • 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. Q. Lü, Y. Wang, An Inverse Source Problem for Semilinear Stochastic Hyperbolic Equations, Submitted. [ArXiv]
  2. Y. Wang, Q. Zhao, Null controllability for semi-discrete stochastic semilinear parabolic equations, Submitted. [ArXiv]
  3. Q. Lü, Y. Wang, Inverse problems for stochastic partial differential equations, Submitted. [ArXiv]
  4. Y. Wang, Q. Zhao, Null controllability for stochastic fourth order semi-discrete parabolic equations, Submitted. [ArXiv]
  5. 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)