Xuguang LU (卢旭光)

Postal Address:

Department of Mathematical Sciences

Tsinghua University

Beijing 100084, P.R. China

E-mail: xglu@math.tsinghua.edu.cn

Phone: +86-10-62788972

Fax:  +86-10-62792401


Brief Curriculum Vitae

Birth Date and Place: Nov. 04, 1955, Liaoning, China.

BS (1982)  Northern Jiaotong University, Beijing.

MS (1986)  Jilin University, Changchun,  Supervisor: Renhong Wang.

PhD (1997)  Tsinghua University, Beijing,  Supervisor: Tianquan Chen.

Positions at Tsinghua University:

Assistant Professor (1986--1988),

Lecturer (1988--1993),

Associate Professor (1993--2001),

Professor (2001--now).

Visiting Experience:

Aug. 2001-- Oct. 2001, Visiting Scholar, Chalmers University of Technology, Göteborg.

Nov. 2001-- Nov. 2002, Visiting Scholar, Georgia Institute of Technology, Atlanta.

Jan. 2006 -- Feb. 2006, Visiting Professor, Université Paris Dauphine, Paris.

Some places of academic talks given in international meetings and workshops:

Beijing (several times since 1995), Atlanta (1999), Oberwolfach (2003, 2010), Zhenjiang (2004),

Shanghai (2005, 2010, 2013), Xining (2006), Wuhan (2008, 2009), UCLA(2009).



Calculus, Mathematical Analysis, Real Analysis, Functional Analysis.

Current teaching:  Mathematical Analysis, Sep. 2012--Jan. 2014.


Research Interest

Current: Kinetic Theory, Classical and Quantum Boltzmann Equations;  Earlier : Approximation Theory of Functions.


Ludwig Boltzmann (1844--1906), Austrian physicist who established the relationship between entropy and the statistical analysis

of molecular motion in 1877, founding the branch of physics known as statistical mechanics. Boltzmann's statistical interpretation

led him to conclude that entropy-decreasing processes were exceedingly improbable but not absolutely impossible. It also paved

the way for the development of quantum mechanics, which is inherently a statistical theory. Boltzmann argued that the equipartition theorem

was a fundamental feature of the kinetic theory. He also derived the "H-theorem " and Boltzmann equation in his paper of 1872.

The H-theorem expresses the increase in entropy of an irreversible process (http://scienceworld.wolfram.com/biography/Boltzmann.html).

For more information see the book "Ludwig Boltzmann: The Man Who Trusted Atoms" written by Carlo Cercignani 

(Oxford University Press, 1998).  This book has been translated into Chinese by Xinhe Hu.



[35] X. Lu, The Boltzmann equation for Bose-Einstein particles: condensation in finite time. J. Stat. Phys. 150 (2013), no. 6, 1138--1176.

[34] X. Lu, On backward solutions of the spatially homogeneous Boltzmann equation for Maxwelian molecules. J. Stat. Phys. 147 (2012), no. 5, 991--1006.

[33] X. Lu and Clément Mouhot, On measure solutions of the Boltzmann equation, part I: moment production and stability estimates. J. Differential Equations 252 (2012), no. 4, 3305-3363.

[32] X. Lu and Xiangdong Zhang, On the Boltzmann equation for 2D Bose-Einstein particles, J. Stat. Phys. 143 (2011), no. 5, 990-1019.

[31] Eric A . Carlen, Maria C. Carvalho and X. Lu,  On strong convergence to equilibrium for the Boltzmann equation with soft potentials. J. Stat. Phys. 135 (2009), no. 4, 681--736.

[30] X. Lu, On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: global existence of weak solutions. J. Differential Equations 245 (2008), no. 7, 1705 --1761.

[29]X. Lu, On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: averaging compactness of weak solutions. J. Stat. Phys. 124 (2006), no. 2-4, 517--547.

[28]X. Lu, The Boltzmann equation for Bose-Einstein particles: velocity concentration and convergence to equilibrium. J. Stat. Phys. 119 (2005), no. 5-6, 1027--1067.

[27] X. Lu, On isotropic distributional solutions to the Boltzmann equation for Bose-Einstein particles. J. Statist. Phys. 116 (2004), no. 5-6, 1597--1649.

[26] Eric A. Carlen and X. Lu,  Fast and slow convergence to equilibrium for Maxwellian molecules via Wild sums,  J. Statist. Phys. 112 (2003), no. 1-2, 59--134.

[25] X. Lu and Bernt Wennberg,  On stability and strong convergence for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles,  Arch. Rational Mech. Anal. 168 (2003), no.1, 1--34.

[24] Yingkui Zhang and X. Lu,  Boltzmann equations with quantum effects II. Entropy identity, existence and uniqueness of spatial decay solutions, Tsinghua Sci. Technol. 7 (2002), no. 3, 219--222.

[23] Yingkui Zhang and X. Lu,  Boltzmann equations with quantum effects I. Long time behavior of spatial decay solutions,  Tsinghua Sci. Technol. 7 (2002), no. 3, 215--218.

[22] X. Lu and Bernt Wennberg ,  Solutions with increasing energy for the spatially homogeneous Boltzmann equation,  Nonlinear Anal. Real World Appl. 3 (2002), no. 2, 243--258.

[21] X. Lu and Yingkui Zhang,  On nonnegativity of solutions of the Boltzmann equation,  Transport Theory Statist Phys. 30 (2001), no. 7, 641--657.

[20] X. Lu,  On spatially homogeneous solutions of a modified Boltzmann equation for Fermi-Dirac particles,  J. Statist. Phys. 105 (2001), no. 1-2, 353--388.

[19] X. Lu,  A modified Boltzmann equation for Bose-Einstein particles: Isotropic solutions and long-time behavior, J. Statist Phys. 98 (2000), no.5-6, 1335--1394.

[18] X. Lu, Conservation of energy, entropy identity, and local stability for the spatially homogeneous Boltzmann equation, J. Statist Phys. 96 (1999), no. 3-4, 765--796.

[17] X. Lu, Spatial decay solutions of the Boltzmann equation: converse properties of long time limiting behavior,  SIAM J. Math. Anal. 30 (1999), no. 5, 1151--1174

[16] X. Lu,  A direct method for the regularity of the gain term in the Boltzmann equation,  J. Math.Anal. Appl. 228 (1998), no. 2, 409--435.

[15] X. Lu,  A result on uniqueness of mild solutions of Boltzmann equations,  Proceedings of the Fourteenth International Conference on Transport Theory (Beijing, 1995).  Transport Theory Statist Phys. 26 (1997), no. 1-2, 209--220.

[14] Hongxing Zou, X. Lu, Qionghai Dai, and Yanda Li, Nonexistence of cross-term free time-frequency distribution with concentration of Wigner-Ville distribution, Sci. China Ser. F 45 (2002), no. 3, 174--180.

[13] X. Lu,  Interpolation inequalities and decay estimates for derivatives,  Approx. Theory Appl. (N.S.) 16 (2000), no. 3, 10--31.

[12] Simin He, X. Lu, and Bo Zhang,  Performance evaluation of partition-based initial point strategy in local search, Chinese J. Computers 21 (1998) Suppl., 73--78. ( in Chinese)

[11] Dayong Cai and X. Lu,  On inhomogeneous eigen problems and pseudospectra of matrices, Scientific computing (Hong Kong, 1997), 49--57, Springer, Singapore, 1997.

[10] X. Lu,  Series representation of Daubechies' wavelets, J. Comput. Math.15 (1997),  no. 1, 81--96.

[9] X. Lu,  Markov-Bernstein type inequalities of multivariate polynomials with positive coefficients and applications,  Approx. Theory Appl. (N.S.) 12 (1996), no. 4, 46--66.

[8] X. Lu, A negative result on multivariate convex approximation by positive linear operators, J. Approx. Theory  86 (1996), no. 1, 108--119.

[7] X. Lu,  Matrix inhomogeneous eigenvalue analysis, (Chinese) Math. Numer. Sinica 16 (1994), no. 3, 319--332;  translation in Chinese J. Numer. Math. Appl. 16 (1994), no. 4, 75--91.

[6] X. Lu, On shape preserving extension and approximation of functions,  Approx. Theory Appl. 8 (1992), no. 2, 67--88.

[5] X. Lu,  On $L\sb 1$-mean approximation to convex functions by positive linear operators, Approximation, optimization and computing, 143--146, North-Holland, Amsterdam, 1990.

[4] X. Lu,  Convex approximation by multivariate polynomials, (Chinese) Math. Numer. Sinica 12 (1990), no. 2, 186--193; translation in Chinese J. Numer. Math. Appl. 12 (1990), no. 3, 59--69.

[3] Renhong Wang and X. Lu,  On dimensions of spaces of bivariate splines with triangulations,  Sci. China Ser. A. 32 (1989), no. 6, 674--684.

[2] X. Lu,  On shape preserving approximation by multivariate positive linear operators, J. Tsinghua Univ. 28 (1988), No. S6, 93-101 (in Chinese).

[1] X. Lu,  On the order of Bernstein polynomial approximation of multivariate convex functions,  (Chinese) Math. Numer. Sinica 10 (1988), no. 4, 398--407; translation in Chinese J. Numer. Math. Appl. 11 (1989), no. 1, 33--42.