Chinese Version
Books
[1]
X. Zhang, Exact Controllability of
Semi-linear Distributed Parameter Systems, Gaodeng Jiaoyu Chubanshe (Higher
Education Press), Beijing,
2004. (In Chinese). 144 pages. ISBN: 7-04-012953-1.
[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.
Invited Reviews
[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.
Articles published in conference proceedings
[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.
Articles published in Journal
[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: Acta Math. Sin. (Engl. Ser.),, 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: Zhongguo Kexue
A Ji-Shuxue, 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.
Chinese
version: Zhongguo Kexue
A Ji-Shuxue,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.
Other Articles
[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.
(http://tcct.amss.ac.cn/newsletter/2014/201407 /xzhang.html). (In
Chinese)
[3]
X. Zhang, A brief probe into
mathematical control theory. Preprint. (In Chinese).
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