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English Version
专 著
[1] 张旭，半线性分布参数系统的精确能控性，高等教育出版社，北京，2004。
[2] Q. Lü
and X. Zhang, General Pontryagin-Type Stochastic Maximum Principle and Backward
Stochastic Evolution Equations in Infinite Dimensions, Springer
Briefs in Mathematics, Springer, Cham, 2014. 146 pages.
[3] X. Fu, Q. Lü and X. Zhang, Carleman Estimates for Second Order Partial Differential
Operators and Applications, a Unified Approach, Springer Briefs in
Mathematics, Springer, Cham. In press.
[4] Q. Lü
and X. Zhang, Mathematical Theory for Stochastic Distributed Parameter
Control Systems, Accepted.
邀请报告
[1] X. Zhang, Recent
progress on exact controllability theory of the wave and plate equations,
Boletin de la Sociedad
Española de Matemática Aplicada, 2004, no. 28, 99–128.
[2] X. Zhang, A unified controllability/observability theory
for some stochastic and deterministic partial differential equations,
Proceedings of the International Congress of Mathematicians, Vol. IV, Hyderabad,
India, 2010, 3008–3034.
会议论文
[1] X. Zhang, Exact internal
controllability of Maxwell equations,
Proceedings of the 17th Chinese Control Conference (1997, Lushan), Wuhan Press, 423–433.
[2] L. Pan, K. L. Teo and X. Zhang,
State observation problem of a class of semilinear hyperbolic systems, Proceedings of The 14th
World Congress of IFAC (1999, Beijing), Vol:
E (Robust Control), Pergamon, 219–224.
[3] X. Zhang, Observability
estimate: a direct method, Proceedings of the 19th Chinese Control Conference (2000, Hong Kong), Vol: 1, 181–186.
[4] X. Zhang and E. Zuazua, The linearized Benjamin-Bona-Mahony
equation: a spectral approach to unique continuation, Semigroups of
Operators: Theory and Applications(Rio de Janeiro,
2001), C. Kubrusly et
al., eds., 368-379, Optimization Software, New York, 2002.
[5] X. Zhang and E. Zuazua, Controllability of nonlinear partial differential equations,
in Lagrangian and Hamiltonian methods for
nonlinear control 2003, 239–243, IFAC,Laxenburg, 2003.
[6] I. Lasiecka, R. Triggiani and X. Zhang, Nonconservative
Schrödinger equations with unobserved Neumann B. C.: Global uniqueness
and observability in one shot, in Analysis and Optimization of
Differential Systems (Constanta, 2002), V. Barbu et al., eds.,Kluwer
Acad. Publ., Boston, MA, 2003, 235–246.
[7] X. Zhang, Global exact
controllability of semi-linear time reversible systems in infinite
dimensional space, Cohen, Gary C. (ed.) et al., Mathematical and
numerical aspects of wave propagation, WAVES 2003, Proceedings of the sixth
international conference on mathematical and numerical aspects of wave
propagation, Jyväskylä, Finland, 30, June-4
July 2003, Berlin, Springer, 183–188 (2003).
[8] X. Zhang and E. Zuazua, Exact controllability of the semi-linear wave equation,in Sixty Open Problems in the Mathematics of
Systems and Control, edited by V. D. Blondel and A. Megretski, Princeton University Press, 2004, 173–178.
[9] X. Zhang, Some progresses
on inverse hyperbolic problem, Proceedings of the 22th Chinese Control
Conference (2003, Yichang), Wuhan University of Technology Press, 389–392.
[10] X. Zhang and E. Zuazua, Stability and control on a model in fluid-structure
interaction, Proceedings of the 22th Chinese Control Conference (2003, Yichang), Wuhan, University
of Technology Press,
22-26.
[11] W. Li and X. Zhang, Controllability
of parabolic and hyperbolic equations: towards a unified theory, in
Control theory of partial differential equations, Lect. Notes Pure Appl. Math.,
242, Chapman & Hall/CRC, Boca Raton, FL, 2005, 157-174.
[12] J. Yong and X. Zhang, Exact
controllability of the heat equation with hyperbolic memory kernel, in
Control theory of partial differential equations, Lect. Notes Pure Appl.Math., 242, Chapman & Hall/CRC, Boca Raton,
FL, 2005, 387–401.
[13] X. Zhang, Unique continuation for stochastic partial
differential equations and its application, Boletin
de la Sociedad Española de Matematica Aplicada, 2006, no. 34, 251–256.
[14] X. Fu, X. Zhang and E. Zuazua,
On the optimality of the observability inequalities for plate systems
with potentials, in Phase Space Analysis of PDEs, A. Bove,
F. Colombini, and D. Del Santo, eds., Birkhäuser, 2006, 117-132.
[15] Z. Li and X. Zhang, On fuzzy logic and chaos theory-from
an engineering perspective, Ruan, Wang, Kerre (Eds.), Fuzzy Logic-A Spectrum of Theoretical &
Practical Issues, Springer-Verlag, 2006.
[16] X. Zhang and E. Zuazua, Asymptotic behavior of a hyperbolic-parabolic
coupled system arising in fluid-structure interaction, International
Series of Numerical Mathematics, Vol. 154, Birkhäuser, Verlag Basel/Switzerland, 2006, 445–455.
[17] H. Li and X. Zhang, Periodic controllability of evolution
equations, in Proceedings of the 26th Chinese Control Conference, Vol.
2, Press of Beihang University, 2007, 651–655.
[18] X. Zhang, Unique continuation and observability for
stochastic parabolic equations and beyond, in Control Theory and Related
Topics (In Memory of Xunjing Li), S. Tang and
J. Yong, eds., World Sci. Publ., Hackensack, NJ, 2007, 147–160.
[19] X. Zhang and E. Zuazua, On
the optimality of the observability inequalities
for Kirchoff plate systems with potentials in unbounded
domains, in Hyperbolic Problems: Theory, Numerics
and Applications, S. Benzoni-Gavage and D. Serre, eds., Springer,2008,
233–243.
[20] X. Zhang, Observability estimates for stochastic
wave equations, in Proceedings of the 27th Chinese Control Conference,
Vol. 3, Press of Beihang University,
2008, 598–600.
[21] X. Zhang, C. Zheng and E. Zuazua,
Exact controllability of the time discrete wave equation: a multiplier
approach, in Applied and Numerical PDEs: Scientific Computing in
Simulation, Optimization and Control and its Multiphysics
Applications, W. Fitzgibbon,
Yu. Kuznetsov, P. Neittaanmäki, J. Periaux and O. Pironneau, eds.,
Computational Methods in Applied Sciences, vol. 15, Springer, Dordrecht, Heidelberg, London, New York, 2010, 229–245.
[22] X. Zhang, Remarks on the controllability of some quasilinear equations,in Some Problems on Nonlinear Hyperbolic Equations
and Applications, T.-T. Li, Y. Peng and B.Rao, eds., Series in Contemporary Applied
Mathematics, vol. 15, Higher Education Press, Beijing, 2010, 437–452.
期刊论文
[1] X. Zhang and F. Li, Existence, uniqueness and
limit behavior of solutions to a nonlinear boundary-value problem with
equivalued surface, Nonlinear Anal., 34(1998), no.4,
525–536.
[2] X. Zhang, Rapid exact controllability of the semilinear wave equation, Chin. Ann.Math. Ser. B, 20 (1999), no. 3, 377–384.
[3] X. Zhang, Solvability of nonlinear parabolic boundary
value problem with equivalued surface, Math.
Meth. Appl. Sci., 22 (1999), no. 3, 259–265.
[4] X. Zhang, Exact internal controllability of Maxwell
equations, Appl. Math. Optim., 41 (2000),
no. 2, 155–170.
[5] X. Zhang, Explicit observability estimate for the
wave equation with potential and its application, Royal Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 456 (2000), no.1997, 1101–1115.
[6] X. Zhang, Uniqueness of weak solution for nonlinear
elliptic equations in divergence form, Internat.
J. Math. and Math. Sci., 23 (2000),
no. 5, 313–318.
[7] A. López, X. Zhang and E. Zuazua, Null controllability of the heat equation
as singular limit of the exact controllability of dissipative wave
equations, J. Math. Pures Appl., 79(2000), no. 8, 741–808.
[8] Y. Tang and X. Zhang, A note on the singular limit of
the exact internal controllability of dissipative wave equations, Acta Math. Sin. (Engl. Ser.), 16 (2000), no.4, 601-612. Shortened Chinese version: 数学学报, 45 (2002), no. 1,108–116.
[9] X. Zhang, Exact controllability of semilinear evolution systems and its applications,
J. Optim. Theory Appl., 107 (2000), no. 2, 415–432.
[10] L. Li and X. Zhang, Exact controllability for semilinear wave equations, J. Math. Anal.
Appl., 250
(2000), no. 2, 589–597.
[11] X. Zhang, Explicit observability inequalities for
the wave equation with lower order terms by means of Carleman
inequalities, SIAM J. Control Optim.,
39(2000), no. 3, 812–834.
[12] X. Zhang, Exact controllability of the semilinear plate equations, Asymptot. Anal., 27(2001), no. 2, 95–125.
[13] M. Yamamoto and X. Zhang, Global uniqueness and
stability for an inverse wave source problem with less regular data,
J. Math. Anal. Appl., 263 (2001), no. 2, 479–500.
[14] X. Zhang, A remark on null exact controllability of
the heat equation, SIAM J. Control Optim., 40 (2001), no. 1, 39–53.
[15] K. Liu, B. Rao and X. Zhang, Stabilization of the
wave equations with potential and indefinite damping, J. Math.
Anal. Appl., 269 (2002), no. 2, 747–769.
[16] X. Zhang and E. Zuazua, Unique continuation for the
linearized Benjamin-Bona-Mahony equation with
space-dependent potential, Math. Ann., 325 (2003),no. 3, 543–582.
[17] X. Zhang and E. Zuazua, Decay
of solutions of the system of thermoelasticity of
type III, Commun. Contemp. Math., 5 (2003), no. 1, 25–83.
[18] K. Liu, M. Yamamoto and X. Zhang, Observability
inequalities by internal observation, J. Optim.
Theory Appl., 116 (2003), no. 3, 621–645.
[19] X. Zhang and E. Zuazua, Polynomia l decay and control
of a 1- d model for fluid-structure interaction, C. R. Math. Acad. Sci.
Paris, 336
(2003), 745–750.
[20] X. Zhang and E. Zuazua, Control, observation and
polynomial decay for a coupled heat-wave system, C. R. Math. Acad. Sci.
Paris, 336 (2003), 823–828.
[21] M. Yamamoto and X. Zhang, Global uniqueness and
stability for a class of multidimensional inverse hyperbolic problems
with two unknowns, Appl. Math. Optim., 48(2003), no. 3, 211–228.
[22] I. Lasiecka, R. Triggiani and X. Zhang, Global uniqueness, observability
and stabilization of nonconservative Schrödinger
equations via pointwise Carleman
estimates.Part I: H_1(Ω)-estimates, J. Inverse
Ill-Posed Problems, 12 (2004), no. 1, 43–123.
[23] I. Lasiecka, R. Triggiani and X. Zhang, Global uniqueness, observability
and stabilization of nonconservative Schrödinger
equations via pointwise Carleman
estimates. Part II: L_2(Ω)-estimates, J. Inverse and Ill-Posed Problems, 12(2004), no. 2, 183–231.
[24] L. Pan, K. L. Teo and X. Zhang,
State-observation problem for a class of semi-linear hyperbolic systems
(Chinese), Chinese Ann. Math. Ser. A, 25 (2004), no. 2, 189–198.
English version: Chinese Journal of
Contemporary Mathematics, 25 (2004), no. 2, 163–172.
[25] X. Zhang and E. Zuazua, Polynomial
decay and control of a 1-d hyperbolic-parabolic coupled system, J.
Differential Equations, 204 (2004), no. 2, 380–438.
[26] L. C. Wang and X. Zhang, Inequalities generated by
chains of Jensen inequalities for convex functions, Kodai
Math. J., 27 (2004), no. 2, 114–133.
[27] S. Tang and X. Zhang, Carleman
inequality for backward stochastic parabolic equations with general coeffcients, C. R. Math. Acad. Sci. Paris, 339 (2004), no. 11, 775–780.
[28] J. Rauch, X. Zhang and E. Zuazua,
Polynomial decay of a hyperbolic-parabolic coupled system, J.
Math. Pures Appl., 84 (2005), no. 4, 407–470.
[29] B. Guo and X. Zhang, The regularity
of multi-dimensional wave equation with partial Dirichlet
control and observation, SIAM J. Control Optim.,
44 (2005), no. 5, 1598–1613.
[30] L. Pan, X. Zhang and Q. Chen, Approximate solutions to
infinite dimensional LQ problems over infinite time horizon, Science in
China Series A-Mathematics, 49 (2006), no. 7, 865–876.
Chinese version: 中国科学 A辑-数学, 36 (2006),
no. 5, 588-600.
[31] X. Zhang and E. Zuazua, A sharp observability
inequality for Kirchoff plate systems with
potentials, Comput. Appl. Math.,
25 (2006), no. 2-3, 353–373.
[32] L. C. Wang and X. Zhang, New inequalities related to
the Jensen-type inequalities with repetitive sample, Int. J. Appl. Math.
Sci., 3 (2006), no. 1, 51–67.
[33] X. Zhang and E. Zuazua, Long
time behavior of a coupled heat-wave system arising in fluid-structure interaction,
Arch. Ration. Mech. Anal., 184 (2007), no. 1, 49–120.
[34] K. Phung, G. Wang and X. Zhang,
On the existence of time optimal control of some linear evolution
equations, Discrete Contin. Dyn.
Syst. Ser. B, 8(2007), no. 4, 925–941.
[35] X. Fu, J. Yong and X. Zhang, Exact controllability for
the multidimensional semilinear hyperbolic equations,
SIAM
J. Control Optim., 46 (2007), no. 5, pp.
1578–1614.
[36] T. Duyckaerts, X. Zhang and E.
Zuazua, On the optimality of the observability
inequalities for parabolic and hyperbolic systems with potentials, Ann.
Inst. H. Poincaré Anal. Non Linéaire,
25 (2008), no. 1, pp. 1–41.
[37] X. Zhang, Unique continuation for stochastic parabolic
equations, Differential Integral Equations, 21 (2008), no. 1-2 , pp. 81–93.
[38] K. Phung and X. Zhang, Time
reversal focusing of the initial state for Kirchoff
plate, SIAM J. Appl. Math., 68 (2008), no. 6, pp. 1535–1556.
[39] X. Zhang, Carleman and observability estimates for stochastic wave
equations, SIAM
J. Math. Anal., 40(2008) no. 2, pp.
851–868.
[40] X. Zhang, C. Zheng and E. Zuazua,
Time discrete wave equations: boundary observability and control, Discrete
Contin. Dyn. Syst., 23
(2009), no.1&2, pp.571-604.
[41] S. Tang and X. Zhang,
Null Controllability for forward and backward stochastic parabolic equations,
SIAM
J. Control Optim., 48 (2009), no. 4,
pp. 2191–2216.
[42] X. Fu, J. Yong and X. Zhang, Controllability and observability
of the heat equations with hyperbolic memory kernel, J. Differential
Equations,247 (2009), no. 8, pp.2395-2439.
[43] X. Liu and X. Zhang,
On the local controllability of a class of multidimensional quasi-linear
parabolic equations, C. R. Math. Acad. Sci. Paris,347
(2009), no. 23-24, 1379-1384.
[44] H. Li, Q. Lü and X. Zhang, Recent
progress on controllability /observability for systems governed by
partial differential equations, J. Syst. Sci. Complex.,23 (2010), no.
3, pp. 527-545.
[45] P. Wang and X. Zhang, Range inclusion of operators on
non-archimedean Banach
space, Science in China Series A-Mathematics, 53(2010), no. 12, 3215-3224.
中文版: 中国科学A辑-数学, 40 (2010), no. 12, 1187-1196.
[46] J. Yong and X. Zhang, Heat equation with memory in anisotropic
and non-homogeneous media, Acta Math. Sin.
(Engl. Ser.), 27 (2011), no. 2, 219-254.
[47] P. Wang and X. Zhang, Numerical solutions of backward
stochastic differential equations: a finite transposition method, C. R.
Math. Acad. Sci. Paris, 349(2011), no.15-16, pp.901-903.
[48] Q.Lü, J.Yong
and X.Zhang, Representation of Itô integrals by Lebesgue/ Bochner integrals, J. Eur. Math. Soc., 14 (2012),
no. 6, 1795–1823.
[49] X. Liu and X. Zhang,
On the local controllability of a class of multidimensional quasi-linear
parabolic equations, SIAM
J. Control Optim., 50 (2012), no. 4,
2046–2064.
[50] X. Liu and X. Zhang, The weak maximum principle for some
strongly coupled elliptic differential systems, J. Funct.
Anal., 263 (2012), no. 7, 1862–1886.
[51] Q. Lü and X. Zhang, Well-posedness of backward stochastic differential equations
with general filtration, J.
Differential Equations, 254 (2013), no. 8, 3200–3227.
[52] X. Fu, X. Liu and and X. Zhang,
Recent progress on controllability of multidimensional quasilinear parabolic systems, J. Control Theory Appl., 68 (2015), no. 6,
948–963.
[53] Q. Lü and X. Zhang, Global
uniqueness for an inverse stochastic hyperbolic problem with three unknowns,
Comm. Pure Appl. Math., 68 (2015),
no. 6, 948–963.
[54] Q. Lü and X. Zhang, Transposition
method for backward stochastic evolution equations revisited, and its
application, Mathematical
Control and Related Fields, 5 (2015), no. 3, 529–555.
[55] H. Zhang and X. Zhang, Pointwise
second-order necessary conditions for stochastic optimal controls, Part
I: The case of convex control constraint, SIAM J. Control Optim., 53 (2015),
no. 4, 2267–2296.
[56] H. Zhang and X. Zhang, Some results on pointwise second-order necessary conditions for
stochastic optimal controls, Science
China Mathematics, 59 (2016), no. 2, 227–238.
[57] Q. Cui, L. Deng and X. Zhang, Pointwise
second order necessary conditions for optimal control problems evolved on
Riemannian manifolds, C. R.
Math. Acad. Sci. Paris, 354 (2016), no. 2, 191–194.
[58] X. Fu, X. Liu and X. Zhang, Controllability of quasilinear complex Ginzburg-Landau
equations (in Chinese), Sci.
Sin. Math., 46 (2016), no. 10, 1425–1444.
[59] X. Fu, X. Liu, Q. Lü and X.
Zhang, An internal observability estimate
for stochastic hyperbolic equations, ESAIM: Control, Optimisation and
Calculus of Variations, 46 (2016), no. 10, 1425–1444.
[60] Q. Lü, X. Zhang and E. Zuazua, Null controllability for wave equation with
memory, J. Math. Pures Appl., 108 (2017), no. 4, 500–531.
[61] H. Frankowska, H. Zhang and
X. Zhang, First and second order necessary conditions for stochastic
optimal controls, Journal of
Differential Equations, 262 (2017), no. 6, 3689–3736.
[62] F. W. Chaves-Silva, X. Zhang and E. Zuazua,
Controllability of evolution equations with memory, SIAM J. Control Optim.,
55 (2017), no. 4, 2437–2459.
[63] H. Zhang and
X. Zhang, Pointwise second-order necessary
conditions for stochastic optimal controls, Part II: The general case,
SIAM J. Control Optim.,
55 (2017), no.5, 2841–2875.
[64] Q. Lü, T. Wang and X. Zhang, Characterization
of optimal feedback for stochastic linear quadratic control problems,
Probab. Uncertain. Quant. Risk 2 (2017),
Paper No. 11, 20 pp.
[65] Q. Lü and X. Zhang, Operator-valued
backward stochastic Lyapunov equations in infinite
dimensions, and its application, Math. Control Relat. Fields, 8
(2018), no. 1, 337–381.
[66] H. Zhang and X. Zhang, Second-order necessary conditions
for stochastic optimal control problems, SIAM Rev., 60 (2018), no. 1, 139–178.
[67] H. Frankowska, H. Zhang and X.
Zhang, Stochastic optimal control problems with control and initial-final
states constraints, SIAM J.
Control Optim., 56 (2018), no. 3, 1823–1855.
[68] H. Zhang and X. Zhang, A survey of second order necessary
conditions for stochastic optimal controls (in Chinese). J. Sys. Sci. & Math. Scis., 29 (2019), no. 2, 228–265.
[69] H. Frankowska, H. Zhang and X.
Zhang, Necessary optimality conditions for local minimizers of stochastic
optimal control problems with state constraints, Trans. Amer. Math. Soc., 372 (2019), no. 2, 1289–1331.
[70] J. Yu and X. Zhang, Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems, Science China Mathematics, 62 (2019),
no. 9, 1645–1656.
[71] Q. Cui, L. Deng and X. Zhang, Second order necessary
conditions for optimal control problems on Riemannian manifolds, ESAIM:
Control, Optimisation and Calculus of
Variations, accepted.
[72] Q. Lü, H. Zhang and X. Zhang,
Second order optimality conditions for optimal control problems of stochastic
evolution equations, submitted.
[73] X. Liu, Q. Lü and X. Zhang, Finite
codimensional controllability, and optimal control
problems with endpoint state constraints, submitted.
[74] H. Frankowska and X. Zhang, Necessary
conditions for stochastic optimal control problems in infinite dimensions,
submitted.
[75] Q. Lü and X. Zhang, Optimal
feedback for stochastic linear quadratic control and backward stochastic Riccati equations in infinite dimensions, submitted.
[76] Q. Lü and X. Zhang, Exact controllability
for a refined stochastic wave equation, submitted.
其它论文
[1] J. Yong and X. Zhang, Biography of Xunjing Li, in Outline of Scientific Achievements of Chinese Famous
Scientists in Twenty Century，The Third Sub-Volume of Mathematical Volume,
Y. Wang et al, eds., Science Press, Beijing, 2012, 324{333. (In
Chinese)
[2] X. Zhang, Some
consideration on the development of control discipline, TCCT
Newsletter, 2014, no. 7. (In Chinese)
[3] X. Zhang, A brief probe into mathematical control
theory. Preprint. (In
Chinese).
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