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McMicken College of Arts & Sciences

Department of Mathematical Sciences

Department of Mathematical Sciences

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Bingyu Zhang

Title: Professor
Office: 4510 French Hall
Tel: 513-556-4060
Email: bingyu.zhang@uc.edu

Education

  • Ph. D., University of Wisconsin-Madison, 1990 (Mathematics).

Research Information

Research Interests

Control theory of partial differential equations, nonlinear dispersive waves, 
electromagnetic waves, nonlinear analysis and applied harmonic analysis.

 

Research Support

  • (PI), Bingyu Zhang, Analysis and Control of Nonlinear Dispersive Wave Equations, Simons Foundation. (201615), $35000. 07/01/2011 to 08/31/2016. Status: Active.
  • (PI), Bingyu Zhang, Analysis and control of dispersive wave equations, Simons Foundation. (20161515), $35000. 07/01/2011 to BAD DATE. Status: Active.

Publications

Peer Reviewed Publications

  • Unique continuation property and control for the Benjamin–Bona–Mahony equation on a periodic domain (with L. Rosier),  J. Differential Equations 254 (2013), no. 1, 141–178.
  • Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries Equation on a bounded domain (with G. Kramer and I. Rivas), ESAIM Control Optim. Calc. Var. , 19 (2013), 358--384.
  • Boundary controllability of the Korteweg-de Vries equation on a bounded domain (with E. Cerpa and I. Rivas),  SIAM J. Control and Optimization, 51(2013), 2976--3010
  • Boundary stabilization of the Korteweg-de Vries equation and the Kortweg-de Vries-Burgers equation (with C.  Jia), Acta Applicandae Mathematicae, 118 (2012), 25--47.
  • Control and Stabilization of the Kawahara Equation on a Periodic Domain (with X.-Q. Zhao),
    Communications in Information and Systems, 12 (2012), 77--95.
  • Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain (with I. Rivas and M. Usman), Mathematical Control and Related Fields, 1(2011), no. 1, 61--81.
  • Nonhomogeneous boundary value problems of the KdV equation on a bounded domain (with G.Kramer), Journal Syst. Sci. & Complexity, 23(2010), 499--526.
  • Control and stabilization of the nonlinear Schrödinger equation on rectangles (with L. Rosier) . Math. Models Methods Appl. Sci. 20 (2010), no. 12, 2293–2347
  • Control and stabilization of the Kortweg-de Vries equation on a periodic domain (with L. Rosier and C. Laurent), Comm. Partial Di ff. Eqns. 35(2010), 707-744.
  • Approximating initial-value problems with two-point boundary-value problems: BBM-equation (with Jerry Bona, H. Q. Chen, S. M. Sun), Bulletin of the Iranian Mathematical Society, 36(2010), 1--25.
  • Complex-valued Burgers and KdV-Burgers equations (with N. Khanal, J. H. Wu, J.-M. Yuan), Journal of Nonlinear Science, 20(2010), 341--360.
  • Forced oscillations of a class of nonlinear dispersive wave equations and their stability (with M. Usman), Discrete and Continuous Dynamical Systems, 26 (2010), 1509--1523.
  • Local exact controllability and stabilizability of the nonlinear Schrödinger equation on a bounded interval (with L. Rosier), SIAM J. Control Optim. 48 (2009), no. 2, 972--992.
  • Control and stabilization of the Korteweg-de Vries Equation: recent progresses (with L. Rosier), J. Syst. Sci. & Complexity 22 (2009), 647--682.
  • Control and stabilization of a family of Boussinesq systems (with S. Micu, J. H. Ortega and L. Rosier), Discrete Contin. Dyn. Syst. 24 (2009), no. 2, 273--313.
  • The Korteweg-de Vries equation on a finite domain II (with J. L. Bona and S. M. Sun), Journal of Differential Equations 247 (2009), 2558--2596.
  • Exact boundary controllability of the nonlinear Schroedinger equation (with L. Rosier), . J. Differential Equations, 246 (2009), no. 10, 4129--4153.
  • Null controllability of the complex Ginzburg-Landau equation (with L. Rosier), Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), no. 2, 649--673.
  • Controllability of the Ginzburg-Landau equation (with L. Rosier), C. R. Math. Acad. Sci. Paris,  346 (2008), no. 3-4, 167--172.
  • Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane (with J. Bona and S.-M. Sun), Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 6, 1145--1185.
  • Forced oscillations of a class of nonlinear dispersive wave equations and their stability (with M. Usman), J. Syst. Sci. Complex. 20 (2007), no. 2, 284--292.
  • Boundary smoothing properties of the Korteweg-de Vries equation in a quarter plane and applications (with J. Bona and S.-M. Sun), Dyn. Partial Differ. Equ. 3 (2006), no. 1, 1--69.
  • Global stabilization of the generalized Korteweg-de Vries equation posed on a finite domain (with L. Rosier), SIAM J. Control Optim. 45 (2006), no. 3, 927--956
  • Forced oscillations of a damped Benjamin-Bona-Mahony equation in a quarter plane (with Y.M. Yang), Control Theory of Partial Di erential Equations, Lecture Notes in Pure and Applied Mathematics, vol. 242 (2005), 375-376.
  • On conditional and unconditional well-posedness of nonlinear evolution equations (with J. Bona and S.-M. Sun), Adv. Diff . Eqns., 9 (2004), 241--265.
  • A nonhomogeneous boundary value problem for the KdV equation posed on a nite domain (with J. Bona and S.-M. Sun), Comm. PDEs 28 (2003), 1391--1436.
  • Forced oscillations of a damped KdV equation in a quarter plane (with J. . Bona and S.-M. Sun), Comm. Contemp. Math. 5 (2003), 369--400.
  • A nonhomogeneous boundary value problem for the Korteweg-de Vries equation in a quarter plane (with Jerry. L. Bona and Shuming Sun), Trans. Amer. Math. Soc., 354 (2001), 427 --490.
  • Computable analysis of the Korteweg-de Vries equation (with W. Gay and N. Zhong), Math. Log. Quart. 47 (2001), 93 --110.
  • Forced oscillation of the Korteweg-de Vries-Burgers equation and its stability, Control of Nonlinear Distributed Parameter Systems, Lecture Notes in Pure and Appl. Math., 218 (2001), 337--357.
  • Exact boundary controllability of the Korteweg-de Vries equation, SIAM Cont. & Optim., 37 (1999), 543 --565.
  • Global exact boundary controllability of a class of quasi-linear hyperbolic systems (with T.-S. Li), J. Math. Anal. Appl., 225 (1998), 289--311.
  • Robustness analysis of dynamic inversion control laws applied to nonlinear aircraft pitch-axis models (with Blaise Morton), Nonlinear Analysis Theory, Methods & Applications, 32 (1998), 501-532.
  • Boundary control of a linear thermoelastic beam (with Scott W. Hansen), J. Math. Anal. Appl., 210 (1997), 182-205.
  • A unique continuation result for the nonlinear Schrödinger equation, Proceedings of the Royal Society of Edinburgh, 127A (1997), 191 --205.
  • A finite element method for an initial value inverse problem with over-speci ed boundary data (with T. Lin), Journal of Mathematical Systems, Estimates and Control, 7 (1997), 305-342.
  • Stability of dynamic inversion control laws applied to nonlinear aircraft pitch-axis models (with Blaise Morton and Dale Enns), International Journal of Control, 63 (1996), 1 --25.
  • The initial value problem for the forced Korteweg-de Vries equation (with Jerry L. Bona), Proceedings of the Royal Society of Edinburgh, Section A, 126A (1996), 571--598.
  • Exact controllability and stabilizability of the Korteweg-de Vries equation (with David L. Russell), Transaction of American Mathematical Society, 348 (1996), 3643--3672.
  • Smoothing and decay properties of solutions of the Korteweg-de Vries equation on a periodic domain with point dissipation (with David L. Russell), J. Math. Anal. Appl., 190 (1995), 449 -- 488.
  • A remark on the Cauchy problem for the Korteweg-de Vries equation on a periodic domain, Differential and Integral Equations, 8 (1995), 1191--1204.
  • Taylor series expansion for solutions of the Korteweg-de Vries equation with respect to their initial values, J. Func. Anal., 129 (1995), 293 -- 324.
  • Analyticity of solutions of the generalized Korteweg-de Vries equations with respect to their initial values, SIAM J. Math. Anal., 26 (1995), 1488-1513.
  • On propagation speed of evolution equations, J. Diff. Eqns., 107(1994), 290--309.
  • Controllability and stabilizability of the third order linear dispersion equation on a periodic domain, (with D. L. Russell),  31(1993), 659 --676.
  • Hardy function and unique continuation for evolution equations, J. Math. Anal. Appl., 178(1993), 381--403.
  • Unique continuation for the Korteweg-de Vries equation, SIAM J. Math. Anal., 23(1992), 55-71.
  • Stablisation de l' equation de Korteweg-de Vries (with V. Komornik and D. L. Russell), C. R. Acad. Sci. Paris, 312(1991), 841--843.

  • Lower regularity solutions of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain (with C. Jia and I. Rivas) , Adv. Differential Equations 19 (2014), 559–584. 
     

  • Boundary smoothing properties of the Kawahara equation posed on the finite domain (with X. Zhao), J. Math. Anal. Appl. 417 (2014), no. 2, 519–536. 
  • Global Controllability and Stabilizability of the Kawaraha Equation on a Periodic Domain (with X. Zhao), Mathematical Control and Related Fields, 5 (2015), 335--358.

Peer Reviewed Conference/Workshop Proceedings

  • Well-posedness and control of the Korteweg-de Vries equation on a bounded domain,  Proceedings of  the International Congress of Chinese Mathematicians (ICCM)  2010,  
    AMS/IP Studies in Advanced Mathematics, 51 (2012), 931--956.

Presentations & Lectures

Invited Presentations

  • (10/12/2014). Initial-boundary value problems of the Hamiltonian fifth order KdV equation SERCDE 2014, University of Memphis.
  • (05/23/2014). Maximum regularity principle for evolutionary partial di Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie, Paris, France.
  • (04/03/2014). On boundary value problems of the Korteweg-de Vries equation on a bounded domain International Conference on Control of Partial Differential Equations , Conservatoire National des Arts et Metiers, Paris, France.
  • (12/13/2013). Recent progresses on non-homogeneous boundary value problems of the Korteweg-de Vries equations School of Mathematics and Computer Engineering, Xihua University, Chengdu.
  • (12/10/2013). Recent progresses on non-homogeneous boundary value problems of the Korteweg-de Vries equations School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China.
  • (11/12/2013). Recent progresses on non-homogeneous boundary value problems of the Korteweg-de Vries equations Department of Mathematics, Kyoto University, Japan.
  • (11/07/2013). Maximum regularity principle of conservative evolutionary partial differential equations Graduate School of Mathematical Sciences, Tokyo University, Japan.
  • (10/25/2013). Conditional and unconditional well-posedness of nonlinear evolution equations Center for Nonlinear Studies, Northwestern University, Xian,, China.
  • (10/18/2013). Maximum regularity principle of conservative evolutionary partial differential equations Department of Mathematics, Zhejiang University, Hangzhou, China.
  • (10/08/2013). Control and stabilization of the Korteweg-de Vries equation School of Mathematics, Physics and Information Science, Zhejiang Ocean University, China.
  • (09/27/2013). Maximum regularity principle of conservative evolutionary partial differential equations The Key Laboratory of System and Control, the Institute of System Sciences, CAS, Beijing.
  • (09/15/2013). Conditional and unconditional well-posedness of nonlinear Schr\"odinger equations Yangtze Center of Mathematics, Sichuan University.
  • (08/22/2013). Some remarks on the well-posedness of the nonlinear Schr\"odinger equations School of Mathematics, Northeast Normal University, China.
  • (05/17/2013). Maximum regularity principle of conservative evolutionary partial differential equations the American Institute of Mathematics (AIM).
  • (10/02/2012). Hidden regularities of solutions of the Korteweg-de Vries equation and their applications Analysis and PDE seminar, Department of Mathematics, University of Kentucky, Lexington, Kentucky.
  • (08/03/2012). Hidden regularities of solutions of the Korteweg-de Vries equation and their applications International Conference on Inverse Problems and PDE Control, Chengdu, China.
  • (06/02/2012). Recent progresses on non-homogeneous boundary value problems of the Korteweg-de Vries equation Chongqinq Analysis Meeting III, Chongqing University, Chongqing, China.
  • (05/24/2012). Recent progresses on non-homogeneous boundary value problems of the Korteweg-de Vries equation the Key Laboratory of System and Control Institute of System Sciences, Chinese Academy of Science, Beijing, China.
  • (03/10/2012). Sharp Trace Theorems for Solutions of Dispersive Wave Equations and Their Applications. Special Session on Nonlinear Partial Differential Equations and Applications, 2012 Spring Southeastern Section Meeting, University of South Florida, Tampa, FL March 10-11, 2012 (Saturday - Sunday).
  • (01-2012). Boundary controllability of the KdV equation 2012 Joint Mathematicsl Meetings, AMS Special Session on Nonlinear Analysis of Partial Differential Equation Models in Biology and Chemical Physics, Boston, January 7, 2012.
  • (09/26/2011). On Boundary Control of the Korteweg-de Vries Equation Control of Partial and Differential Equations Days in Orleans , Orleans, France.
  • (03-2011). Non-homogeneous boundary value problems of nonlinear dispersive wave equations Department of Mathematics, Colorado State Unviersity, Fort Collins , Colorado, March 23, 2011.
  • (12-2010). On non-homogeneous boundary value problems of the Korteweg-de Vries equation 2010 International Congress of Chinese Mathematicians, Beijing, December 16--22, 2010.
  • (12-2010). Control and Stabilization of the Nonlinear Schrodinger Equation, The Conference on Mathematics, Analysis and Control in Chemical Physics and Related Systems University of Nevada, Las Vegas, December 14-17, 2010.
  • (12-2010). Introduction to Control of nonlinear PDEs, The Conference on Mathematics, Analysis and Control in Chemical Physics and Related Systems University of Nevada, Las Vegas, December 14-17, 2010.
  • (11-2010). Nonhomogeneous boundary value problems of the nonlinear Schrödinger equation, Workshop on Control of Dispersive Equations Institute Henri Poincaré, Paris, France, November 8--10, 2010.
  • (10-2010). On initial-boundary value problems for the Korteweg-de Vries equation Institute Henri Poincaré, Paris, France, October 29, 2010.
  • (08-2010). On a class of initial-boundary-value problem of the Korteweg-de Vries equation on a bounded domain Yangtze International Mathematics Forum, Chengdu, China, August 8-13, 2010..
  • (03-2010). Control and stabilization of the nonlinear Schrödinger equation on rectangles, Special Session on Analysis and Control of Dispersive Partial Differential Equations 2010 Spring Southeastern Sectional Meeting, Lexington, KY, March 27-28, 2010.
  • (03-2010). Nonhomogeneous boundary value problems of the nonlinear Schr Schrödinger equation Summer School in Mathematics, Universidade Estadual de Maringa, Brazil, March 1-- 5, 2010.

Paper Presentations

  • (03/13/2013). Nonhomogeneous boundary value problems of the nonlinear Schr\"odinger equation. The 3rd Ohio River Analysis Meetin, Cincinnati.

Colloquia

  • (10/19/2012). Hidden regularities of solutions of the Korteweg-de Vries equation and their applications. Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma.
  • (02/10/2012). Non-homogeneous boundary value problems of nonlinear dispersive wave equations. Department of Mathematics, University of Nevada at Las Vegas, February 10,2012.
  • (12-2011). On Recent Progress of Initial-Boundary-Value Problems of Nonlinear Dispersive Wave Equations. Department of Mathematics, University of Texas-Pan American, December 5, 2011.
  • (05-2011). Control and stabilization of the Korteweg-de Vries equation. School of Mathematics, Sichuan Normal University, Chengdu, China, May 24, 2011.
  • (04-2011). Recent progresses of control and stabilization of the KdV equation. Department of Mathematics, Virginia Tech, Blacksburg, Virginia, April 23, 2010.
  • (10-2009). Control and stabilization of the Korteweg-de Vries equation. Department of Mathematics and Statistics, Air Force Institute of Technology, Dayton, Ohio, October 30, 2009.
  • (06/04/2009). Nonhomogeneous boundary value problems of nonlinear dispersive wave equations. School of Mathematics, Sichuan Normal University.
  • (12/03/2007). Non-homgeneous boundary value problems of nonlinear dispersive wave equations. Department of Mathematics, Wayne State University, Detroit, Michigan.
  • (10/28/2006). On Recent Progress of the Initial Boundary Value Problems of the Korteweg-de Vries Equation. Department of Mathematics, Virginia Tech, Blacksburg, Virginia.
  • (03/21/2003). On conditional and unconditional well-posedness for nonlinear evolution equations. Department of Mathematics, Virginia Tech.
  • (10/07/2002). Smoothing properties of nonlinear dispersive wave equations. Department of Mathematics, University of Dayton, Dayton, Ohio.

Experience & Service

Work Experience

  • 1990 to 1995, Asssitant Professor, Department of Mathematical Sciences , University of Cincinnati.
  • 1992 to 1994, Postdoctoral member in industrial mathematics, Institute for Mathematics and Its Applications, University of Minnesota.
  • 1995 to 2000, Associate Professor, Department of Mathematical Sciences , University of Cincinnati.
  • 05-1996 to 06-1996, Visting Professor, Department of Mathematics, University of Strabourg, France.
  • 07-1997Visting Professor, Institue of Elie Cartan, University of Nancy I, France.
  • 01-1998 to 05-1998, Research Fellow, Texas Institute of Computational and Applied Mathematics, University of Texas-Austin.
  • 2000 to Present, Professor, Department of Mathematical Sciences , University of Cincinnati.
  • 05-2001Visting Professor, Texas Institute of Computational and Applied Mathematics, University of Texas-Austin.
  • 06-2003Visting Professor, Institue of Elie Cartan, University of Nancy I, France.
  • 07-2005Visting Professor, Department of Mathematics, University of Strabourg, France.
  • 03-2006 to 04-2006, Visting Professor, Department of Mathematics, University of Illinois at Chicago.
  • 05-2008 to 07-2008, Visting Professor, Laboratoire Jacques -Louis Lions · Université Pierre et Marie Curie, France.
  • 10/01/2010 to 11/30/2010, Visiting Professor, Laboratoire Jacques -Louis Lions · Université Pierre et Marie Curie, Paris, France.
  • 05/01/2014 to 05/31/2014, Visting Professor, Laboratoire Jacques -Louis Lions, Université Pierre et Marie Curie, Paris, France.

Events Organized

  • Workshop. Non-homogeneous boundary value problems of for nonlinear waves (05/13/2013 to 05/17/2013) , the American Institute of Mathematics (AIM), Palo Alto, California.

Service

  • Editorial Board Member, ESAIM: Control, Optimisation and Calculus of Variations 01-2013 to 12-2016
  • Editorial Board Member, Mathematical Control and Related Fields 2010 to Present
  • Editorial Board Member, Journal of Systems Science & Complexity 2009 to Present