# Prof. Qi Lü

School of Mathematics, Sichuan University, China.

Qi Lü (吕琦)

School of Mathematics, Sichuan University, Chengdu 610064, China

E-mail: lu@scu.edu.cn

## Working Experience

• 03.2014–now, full professor, School of Mathematics, Sichuan University.

• 01.2013–01.2014, Post-doc fellow under the supervision of Prof. Jean-Michel Coron in Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie-Paris VI.

• 07.2012-03.2014, Associate Professor, School of Mathematical Sciences, University of Electronic Science and Technology of China.

• 04.2011–04.2012, Post-doc fellow under the supervision of Prof. Enrique Zuazua in Basque Center for Applied Mathematics, Spain.

• 07.2010–07.2012, Assistant Professor, School of Mathematical Sciences, University of Electronic Science and Technology of China.

## Education

• 09.2007–06.2010 PhD Student in School of Mathematics, Sichuan University

• 09.2004–06.2007 Master Degree, School of Mathematics, Sichuan University.

• 09.2000–06.2004 Bachelor Degree, University of Electronic Science and Technology of China.

## Publications

### Books

1. Q. Lü and X. Zhang, General Pontryagin-type stochastic maximum principle and backward stochastic evolution equations in inﬁnite dimensions. Springer, Cham, 2014. [Book]

2. X. Fu, Q. Lü and X. Zhang, Carleman estimates for second order partial differential operators and applications. A unified approach. Springer, Cham, 2019. [Book]

3. Q. Lü and X. Zhang, Mathematical control theory for stochastic partial differential equations. In press, Springer, 2020.

### Articles

1. H. Li, Q. Lü, X. Zhang, Recent progress on controllability/observability for systems governed by partial differential equations. Journal of Systems Science and Complexity. 23 (2010), 527–545. [Article]

2. J. Li, Q. Lü, State observation problem for general time reversible system and applications. Applied Mathematics and Computation 217 (2010), 2843–2856. [Article]

3. Q. Lü, Bang-Bang Principle of Time Optimal Controls and Null Controllability of Fractional Order Parabolic Equations. Acta Mathematica Sinica. 26(2010), 2377–2386. [Article]

4. Q. Lü, Observability estimate for stochastic Schrödinger equations. Comptes rendus - Mathematique. 348(2010), 1159–1162. [Article]

5. Q. Lü, Some results on the controllability of forward stochastic heat equations with control on the drift. Journal of Functional Analysis. 260 (2011), 832–851. [Article]

6. Q. Lü and G. Wang, On the existence of time optimal controls with constraints of the rectangular type for heat equations. SIAM Journal on Control and Optimization. 49 (2011), 1124–1149. [Article]

7. Q. Lü, Carleman estimate for stochastic parabolic equations and inverse stochastic parabolic problems. Inverse Problems. 28(2012), 045008. [Article]

8. Q. Lü, J. Yong and X. Zhang, Representation of Itô integrals by Lebesgue/Bochner integrals. Journal of the European Mathematical Society. 14(2012), 1795–1823. [Article]

9. H. Li, Q. Lü, Null controllability for some systems of two backward stochastic heat equations with one control force. Chinese Annals of Mathematics, Series B 33 (2012), 909–918. [Article]

10. Q. Lü, X. Zhang, Well-posedness of backward stochastic differential equations with general filtration. Journal of Differential Equations. 254 (2013), 3200–3227. [Article]

11. Q. Lü, A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators. ESAIM Control, Optimisation and Calculus of Variations. 19(2013), 255–273. [Article]

12. H. Li, Q. Lü, A quantitative boundary unique continuation for stochastic parabolic equations. Journal of Mathematical Analysis and Applications. 402 (2013), 518–526. [Article]

13. Q. Lü, Observability estimate for stochastic Schrödinger equations. SIAM Journal on Control and Optimization. 51(2013), 121–144. [Article]

14. Q. Lü, Exact controllability for stochastic Schrödinger equations. Journal of Differential Equations. 255(2013), 2484–2504. [Article]

15. Q. Lü, Observability estimate and state observation problems for stochastic hyperbolic equations. Inverse Problems. 29(2013), 095001. [Article]

16. Q. Lü, Z, Yin, The $$L^\infty$$-null controllability of parabolic equation with equivalued surface boundary conditions. Asymptotic Analysis. 83 (2013), 355–378. [Article]

17. Q. Lü, Z, Yin, Recent progress on observability for stochastic partial differential equations. Emerging topics on differential equations and their applications, 94–108, Nankai Series in Pure, Applied Mathematics and Theoretical Physics, 10, World Sci. Publ., Hackensack, NJ, 2013. [Article]

18. Q. Lü, Exact controllability for stochastic transport equations. SIAM: Journal on Control and Optimization. 52(2014), 397–419. [Article]

19. Q. Lü and E. Zuazua, Robust null controllability for heat equations with unknown switching control mode. Discrete and Continuous Dynamical Systems. 34(2014), 4183–4210. [Article]

20. J. M. Coron and Q. Lü, Local rapid stabilization for a KortewegCde Vries equation with a Neumann boundary control on the right. Journal de Mathématiques Pures et Appliquées. 102(2014), 1080–1120. [Article]

21. Q. Lü, X. Zhang, Global uniqueness for an inverse stochastic hyperbolic problem with three unknowns. Communications on Pure and Applied Mathematics. 68 (2015), 948–963. [Article]

22. Q. Lü and Z. Yin, Unique Continuation for Stochastic Heat Equations. ESAIM Control, Optimisation and Calculus of Variations. 21 (2015), 378–398 [Article]

23. J.-M. Coron and Q. Lü, Fredholm transform and local rapid stabilization for a Kuramoto-Sivashinsky equation. Journal of Diﬀerential Equations. 259(2015), 3683–3729. [Article]

24. Q. Lü and X. Zhang, Transposition method for backward stochastic evolution equations revisited, and its application. Mathematical Control and Related Fields. 5 (2015), 529–555 [Article]

25. Q. Lü, Stochastic well-posed systems and well-posedness of some stochastic partial diﬀerential equations with boundary control and observation. SIAM Journal on Control and Optimization. 53(2016), 3457–3482. [Article]

26. Q. Lü and E. Zuazua, Averaged controllability for random evolu-tion partial differential equations. Journal de Mathématiques Pures et Appliquées. 105(2016), 367–414. [Article]

27. Q. Lü and E. Zuazua, On the lack of controllability of fractional in time ODE and PDE. Mathematics of Control, Signals, and Systems. 28 (2016), Art. 10, 21 pp. [Article]

28. E. Fernández-Cara, Enrique,; Q. Lü and E. Zuazua, Null Controllability of Linear Heat and Wave Equations with Nonlocal Spatial Terms. SIAM Journal on Control and Optimization. 54 (2016), 2009–2019. [Article]

29. X. Fu, X. Liu, Q. Lü and X. Zhang, An internal observability estimate for stochastic hyperbolic equations. ESAIM Control, Optimisation and Calculus of Variations. 22(2016), 1382–1411. [Article]

30. Q. Lü, X. Zhang and E. Zuazua, Null controllability for wave equations with memory. Journal de Mathématiques Pures et Appliquées. 108 (2017), 500–531. [Article]

31. Q. Lü, T. Wang, X. Zhang, Characterization of optimal feedback for stochastic linear quadratic control problems. Probability, Uncertainty and Quantitative Risk. 2 (2017), Paper 20 pp. [Article]

32. Q. Lü, J. Yong, X. Zhang, “Erratum to “Representation of Itô integrals by Lebesgue/Bochner integrals” (Journal of the European Mathematical Society. 14, 1795–1823 (2012)). Journal of the European Mathematical Society. (JEMS) 20 (2018), 259–260. [Article]

33. Q. Lü, X. Zhang, Operator-valued backward stochastic Lyapunov equations in infinite dimensions, and its application. Mathematical Control & Related Fields. 8 (2018), 337–381. [Article]

34. Q. Lü, J van Neerven, On conditional expectations in $$L^p(\mu;L^q(\nu;X))$$. Positivity. 23 (2019), 11–19. [Article]

35. F. Dou and Q. Lü, Partial approximate controllability for linear stochastic control systems. SIAM Journal on Control and Optimization. 57 (2019), 1209–1229. [Article]

36. Q. Lü, Well-posedness of stochastic Riccati equations and closed-loop solvability for stochastic linear quadratic optimal control problems. Journal of Differential Equations. 267 (2019), 180–227. [Article]

37. Q. Lü, X. Zhang, A mini-course on stochastic control. Control and inverse problems for partial differential equations, 171–254, Series in Contemporary Applied Mathematics. CAM, 22, Higher Education Press, Beijing, 2019. [Article]

38. Q. Lü, J van Neerven, Backward stochastic evolution equations in UMD Banach spaces. Positivity and noncommutative analysis, 381–404, Trends Math., Birkhäuser/Springer, (2019) [Article]

39. H. Frankowska and Q. Lü, First and second order necessary optimality conditions for controlled stochastic evolution equations with control and state constraints. Journal of Differential Equations 268 (2020), 2949–3015. [Article]

40. F. Dou and Q. Lü, Time-inconsistent linear quadratic optimal control problems for stochastic evolution equations. SIAM Journal on Control and Optimization. 57 (2020), 485–509. [Article]

41. X. Liu, Q. Lü and X. Zhang, Finite codimensional controllability and optimal control problems with endpoint state constraints. Journal de Mathématiques Pures et Appliquées. 138 (2020), 164–203. [Article]

42. Q. Lü and Z. Yin, Local state observation for stochastic hyperbolic equations. ESAIM: Control, Optimisation and Calculus of Variations. https://doi.org/10.1051/cocv/2019049 [Article]

43. Q. Lü, Stochastic linear quadratic optimal control problems for mean-field stochastic evolution equations. ESAIM: Control, Optimisation and Calculus of Variations. 26 (2020) 127. [Article]

44. Q. Lü and X. Zhang, A concise introduction to control theory for stochastic partial differential equations. Mathematical Control & Related Fields. 0 (2021) 0.[Article]

### Preprints

1. Q. Lü, H. Zhang and X. Zhang, Second order optimality conditions for optimal control problems of stochastic evolution equations. arXiv:1811.07337 [Article]

2. Q. Lü and X. Zhang, Optimal feedback for stochastic linear quadratic control and backward stochastic Riccati equations in infinite dimensions, arXiv:1901.00978 [Article]

3. Q. Lü and X. Zhang, Exact controllability for a refined stochastic wave equation, arXiv:1901.06074 [Article]