Bingyu Zhang , PhD
Professor
Professor
French Hall
4504
A&S Mathematical Sciences - 0025
Education
Ph. D.: University of Wisconsin-Madison 1990 (Mathematics)
Research and Practice Interests
Control theory of partial differential equations, nonlinear dispersive waves,
electromagnetic waves, nonlinear analysis and applied harmonic analysis.
Abbreviated Publications
Peer Reviewed Publications
Lower regularity solutions of the non-homogeneous boundary-value problem for a higher order Boussi- nesq equation in a quarter plane (with S. Li, M. Chen and X. Yang). Nonlinear Anal. 221 (2022), Paper No. 112893, 29 pp.
Local well-posedness of the coupled KdV-KdV systems on ℝ (with X. Yang), Evol. Equ. Control Theory 11 (2022), no. 5, 1829–1871
Well-posedness and critical index set of the Cauchy problem for the coupled KdV-KdV systems on 𝕋 (with X. Yang). Discrete Contin. Dyn. Syst. 42 (2022), no. 11, 5167–5199.
Kato smoothing properties of a class of nonlinear dispersive wave equations on a periodic domain (with S. Sun, X. Yang and N. Zhong). ESAIM Control Optim. Calc. Var. 27 (2021), Paper No. 12, 27 pp.
Forced oscillation of viscous Burgers’ equation with a time-periodic force (with T. Wang), Discrete & Continuous Dynamical Systems - B, 26 (2021), 1205-1221
Local exact controllability to the trajectories of the Kortewegde VriesBurgers equation on a bounded domain with mixed boundary conditions (with E. Cerpa and C. Montoya), J. Differential Equations 268 (2020) 4945–4972
Controllability and Stabilizability of a Higher Order Wave Equation on a Periodic Domain (with S. Li and M. Chen), SIAM Journal on Control and Optimization, 58 (2020), 1121-1143.
A Non-homogeneous Boundary Value Problem for the Kuramoto-Sivashinsky Equation Posed in a Finite Interval (with J. Li and Z.X. Zhang), ESAIM: COCV 26 (2020) 43, 1–26.
Low regularity solutions of non-homogeneous boundary value problems of a higher order Boussinesq equation in a quarter plane (with M. Chen and S. Li), J. Math. Anal. Appl., 49 (2020)
Non-homogeneous boundary value problems of the fifth-order KdV equations on a bounded interval (with X. Zhao), J. Math. Anal. Appl. 470 (2019), no. 1, 251–278.
Well-posedness of the sixth order Boussinesq equation with nonhomogeneous boundary value on a bounded domain (with S. Li and M. Chen), Phys. D 389 (2019), 13–23.
Standing lattice wave patterns of a Boussinesq system (with S. Li and M. Chen), Standing lattice wave patterns of a Boussinesq system. J. Math. Fluid Mech. 21 (2019), no. 2, Art. 28, 21 pp.
Standing lattice wave patterns of a Boussinesq system (with S. Li and M. Chen), Standing lattice wave patterns of a Boussinesq system. J. Math. Fluid Mech. 21 (2019), no. 2, Art. 28, 21 pp.
General boundary value problems of the Korteweg-de Vries equation on a bounded domain (with R. A. Capistrano–Filho and S. Sun), Mathematical Control and Related Fields, 8, (2018), no. 3&4, 583–605.
Non-homogeneous boundary value problems for the complex Ginzburg-Landau equation on a finite interval (with J. Li and Z.X. Zhang), Applicable Analysis, 97 (2018), no. 11, 1896–1915.
Well-posedness of the generalized Burgers equation on a finite interval (with J. Li and Z.X. Zhang), Applicable Analysis, on line (2018): DOI: 10.1080/00036811.2018.1471211, 1563-504X (Online) Journal homepage: http:// www.tandfonline.com/loi/gapa20
A non-homogeneous boundary value problem of the sixth order Boussinesq equation in a quarter plane (with S. Li and M. Chen), Discrete & Continuous Dynamical Systems - A , Discrete 38 (2018), no. 5, 2505--2525.
Non-homogeneous boundary value problems of nonlinear Schrodinger quations in a half plane (with Y. Ran and S. Sun), SIAM J. Math. Anal. 50 (2018), no. 3, 2773--2806.
Non-homogeneous boundary value problems of nonlinear Schrodinger equations in a half plane (with Y. Ran and S. Sun), SIAM J. Math. Anal. 50 (2018), no. 3, 2773–2806.
General boundary value problems of the Korteweg-de Vries equation on a bounded domain (with R. A. Capistrano–Filho and S. Sun), Mathematical Control and Related Fields, 8, (2018), no. 3&4, 583–605.
Non-homogeneous boundary-value problems for one-dimensional nonlinear Schrrodinger equation (with J. Bona and S. Sun), Journal de Mathematiques Pures et Appliquees , 109 (2018), 1--66.
A non-homogeneous boundary value problem for the Kuramoto-Sivashinsky equation in a quarter plane
(with J. Li and Z. Zhang), Mathematical Methods in the Applied Sciences, 40 (2017), 5619--5641.
Sun, Shu-Ming; Trélat, Emmanuel; Zhang, Bing-Yu; Zhong, Ning On sharpness of the local Kato-smoothing property for dispersive wave equations. Proc. Amer. Math. Soc. 145(2017), no. 2, 653–664.
Caicedo, Miguel Andres; Zhang, Bing-Yu Well-posedness of a nonlinear boundary value problem for the Korteweg–de Vries equation on a bounded domain. J. Math. Anal. Appl. 448 (2017), no. 2, 797–814.
Neumann boundary controllability of the Korteweg-de Vries equation on a bounded domain (with M.
Caicedo and R. A. Capistrano{Filho), SIAM J. Control Optim. , 55 (2017), 3503--3532.
Initial boundary value problem of the Hamiltonian fifth-order KdV equation on a bounded domain (with D. Zhou). Adv. Differential Equations 21 (2016), no. 9-10, 977–1000.
Global Controllability and Stabilizability of the Kawaraha Equation on a Periodic Domain (with X. Zhao), Mathematical Control and Related Fields, 5 (2015), 335--358.
Global controllability and stabilizability of Kawahara equation on a periodic domain. Math. Control Relat. Fields 5 (2015), no. 2, 335–358.
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), no. 5-6, 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.
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
Jia, Chaohua; Zhang, Bing-Yu Boundary stabilization of the Korteweg-de Vries equation and the Korteweg-de Vries-Burgers equation. Acta Appl. Math. 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 some dispersive wave equations. Nonlinear dispersive wave systems (Orlando, FL, 1991), 347–364, World Sci. Publ., River Edge, NJ, 1992.
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.
Editorial
Preface [Special Issue on "Dedicated to Professor Jerry Bona for his 70th birthday'']. J. Math. Study 49 (2016), no. 2, i. 35-06 (76-06)
Prefaces
Preface [Special Issue on "Dedicated to Professor Jerry Bona for his 70th birthday'']. J. Math. Study 49 (2016), no. 2, i. 35-06 (76-06)
Peer Reviewed Conference/Workshop Proceedings
Service
ESAIM: Control, Optimisation and Calculus of Variations Editorial Board Member Type:Editorial Service Level:International 01-2013 -To Present
Mathematical Control and Related Fields Editorial Board Member Type:Editorial Service Level:International 2010 -To Present
Journal of Systems Science & Complexity Editorial Board Member Type:Editorial Service Level:International 2009 -2020
Keywords
mathematical theory of nonlinear waves; control theory of linear and nonlinear partial differential equations; nonlinear analysis and applied harmonic analysis