Professor in

Academy of Mathematics and Systems Science

The Chinese Academy of Sciences

QUALIFICATION

EMPLOYMENT HISTORY

MAIN RESEARCH GRANTS

A List of Papers

 

36. Uniform decay of local energy for the wave equation with variable coefficients, preprint in 2009.

 

35  Boundary Controllability for the quasilinear wave equation, to appear in  Appl. Math. Optim.

 

34  On shallow shell equations,  Discrete and Continuous Dynamical Systems Series,  Vol. 2, No. 3, September 2009,  pp. 697-722.

 

33 Global smooth solutions and stabilization of nonlinear elastodynamic systems with locally distributed dissipation (with Zhi-Fei Zhang),  Systems & Control Letters 58(2009) 491-498.

 

32  Decay of energy for the Cauchy problem of the linear wave equation of variable coeffcients with dissipation, to appear in  Chin. Ann. Math.

 

31 Global smooth solutions of the quasi-linear wave equation with internal velocity feedback (with Zhi-Fei Zhang), SIAM J. Control Optim. 47 (2008), no. 4, 2044-2077.

 

30  Global smooth solutions for the quasilinear wave equation with boundary dissipation, J. Differential Equations 241 (2007), no. 1, 62-93.

 

29 An energy-preserving nonlinear system modeling a string with input and output on the boundary. Nonlinear Anal. 66 (2007), no. 10, 2128-2139.

 

28  Global smooth solutions and exponential stability for a nonlinear beam (with Weiss George), SIAM J. Control Optim. 45 (2007), no. 6, 1931-1964.

 

27  Stabilization of Euler-Bernoulli plate equation with variable coefficients by nonlinear boundary feedback (with Yuxia Guo), J. Math. Anal. Appl. 317 (2006), no. 1, 50-70.

 

26  Carleman estimates for a plate equation on a Riemann manifold with energy level terms (with Lasiecka, I.; Triggiani, R.)  Analysis and applications---ISAAC 2001 (Berlin), 199-236, Int. Soc.

Anal. Appl. Comput., 10, Kluwer Acad. Publ., Dordrecht, 2003.

 

25  Observability inequalities for thin shells (with Shugen Chai). Sci. China Ser. A 46 (2003), no. 3, 300-311.

 

24   Boundary feedback stabilization of shallow shells (with Shugen Chai and Yuxia Guo). SIAM J. Control Optim. 42 (2003), no. 1, 239-259.

 

23  On boundary stability of wave equations with variable coefficients (with Yuxia Guo). Acta Math. Appl. Sin. Engl. Ser. 18 (2002), no. 4, 589-598.

 

22  Carleman estimates with no lower-order terms for general Riemann wave equations. Global uniqueness and observability in one shot. Special issue dedicated to the memory of Jacques-Louis Lions (with Triggiani, R.).  Appl. Math. Optim. 46 (2002), no. 2-3, 331-375.

 

21  Stabilization of elastic plates with variable coefficients and dynamical boundary control (with Yuxia Guo and Shugen Guo).  Quart. Appl. Math. 60 (2002), no. 2, 383-400.

 

20  The ellipticity of the elliptic membrane.  Acta Anal. Funct. Appl. 3 (2001), no. 4, 322-333.

 

19. Observability inequalities for the Euler-Bernoulli plate with variable coefficients. Differential geometric methods in the control of partial differential equations (Boulder, CO, 1999), 383-406,

Contemp. Math., 268, Amer. Math. Soc., Providence, RI, 2000.

 

18. Observability inequalities for shallow shells. SIAM J. Control Optim. 38 (2000), no. 6, 1729-1756.

 

17. On the dual boundary conditions and the nonnegative square root of the second derivative operator.  J. Differential Equations 162 (2000), no. 2, 270-299.

 

16.  Inverse/observability estimates for Schrodinger equations with variable coefficients (with Triggiani, R.). Recent advances in control of PDEs. Control Cybernet. 28 (1999), no. 3, 627-664.

 

15.   An observability estimate in $L\sb 2(\Omega)\times H\sp{-1}(\Omega)$ for second-order hyperbolic equations with variable coefficients (with Lasiecka, I and Triggiani, R.). Control of

distributed parameter and stochastic systems (Hangzhou, 1998), 71-78, Kluwer Acad. Publ., Boston, MA, 1999.

 

14. Inverse/observability estimates for second-order hyperbolic equations with variable

coefficients (with Lasiecka,I and Triggiani, R.). J. Math. Anal. Appl. 235 (1999), no. 1, 13-57.

 

13.  On the observability inequalities for exact controllability of wave equations with variable coefficients.  SIAM J. Control Optim. 37 (1999), no. 5, 1568-1599.

 

12. On the nonnegative square root of the fourth derivative operators. J. Differential Equations148 (1998), no. 2, 318-333.

 

11. Exact controllability for second-order hyperbolic equations with variable coefficient-principal part and first-order terms (with Lasiecka, I and Triggiani, R.). Proceedings of the Second World

Congress of Nonlinear Analysts, Part 1 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 1, 111-122.

 

10. Structure for nonnegative square roots of unbounded nonnegative selfadjoint operators (with De-Xin Feng). Quart. Appl. Math. 54 (1996), no. 3, 457-473.

 

9. On the dual boundary conditions of the fourth derivative operators.  Quart. Appl. Math. 54 (1996), no. 3, 445-456.

 

8  Paley-Wiener theorem and asymptotic behavior of $C\sb 0$ semigroups (with De-Xin Feng).  Acta Math. Sinica (N.S.) 11 (1995), Special Issue, 153-162.

 

7. On the inversion of the Laplace transform of $C\sb 0$ semigroups and its applications. SIAM J. Math. Anal. 26 (1995), no. 5, 1331-1341.

 

6  A characteristic condition for the exponential stability of $C_0$ semigroup (with De-Xin Feng),  Chinese Science Bulletin, Vol.39, No. 7 (1994), 534-537.

 

5.  The number of positive solutions to an integral equation with double rank kernel. (Chinese) Acta Math. Sci. (Chinese) 11 (1991), no. 3, 2.

 

4.  The convergence of an algorithm (with Jinsheng Xiu). (Chinese), Math. Numer. Sinica 12 (1990), no. 2, 221-224

 

3. Perturbations of a class of linear operators. (Chinese) Acta Math. Sinica 31 (1988), no. 5, 615-622.

 

2.  Perturbation of rank one for a class of linear operators(with Chang Kai Liu and Guangtian Zhu). (Chinese)  J. Systems Sci. Math. Sci. 7 (1987), no. 1, 78-88.

 

1. The pole assignment problem for a class of linear operators.(Chinese)  J. Systems Sci. Math. Sci. 5 (1985), no. 2, 145-150.

QUALIFICATION

EMPLOYMENT HISTORY

A LIST of PAPERS

MAIN RESEARCH GRANTS

Research Interests:

● Control and Modeling of Vibrational Mechanics

● Scattering problem for Vibrational systems

● Global and blow-up solutions

RESEARCH INTERESTS