Professor Tong Yang

Professor Tong Yang  

          Chair Professor of Mathematics
          Associate Dean of College of Science and Engineering

          Office: Room Y6513, Academic Building
          Telephone: (852) 2788 9819
          Fax: (852) 2788 7446
          E-mail: matyang@cityu.edu.hk 
          Address: Department of Mathematics
                          City University of Hong Kong
                          83 Tat Chee Avenue, Kowloon, Hong Kong

Education

          PhD in Mathematics, University of California, Davis, June, 1993

          PhD Thesis Advisor: Blake Temple

          Some pictures with my advisors and friends

　

 

Research Areas

  1. Conservation laws: Well-posedness theory, structure of solutions, multi-dimensional problems, stability of nonlinear wave patterns and solution profiles, singularity analysis, numerical schemes.
  2. Boltzmann equation: Phenomena related to fluid dynamics such as nonlinear wave patterns and solution profiles, boundary layer theory, time-periodic solutions and convergence rates, solutions in new function spaces, hypocoercivity problems, regularity of non cutoff cross-sections.

  

Editorial Board

  1. Kinetic and Related Models, Co-editor-in-chief.
  2. Acta Mathematicae Applicatae Sinica (Chinese Series), Editor.
  3. Analysis and Applications, Editor.
  4. Communications on Pure and Applied Analysis, Editor.

Publications:

Ⅰ. Lecture Notes

  1. Seiji Ukai, Tong Yang, Mathematical Theory of Boltzmann Equation, Lecture Notes Series-No. 8, Liu Bie Ju Centre for Math. Sci., City University of Hong Kong, 2006. 
  2. Seiji Ukai, Tong Yang, Conservation Laws and Kinetic Theory, Lectures on Conservation Laws and Related Topics, Ed. Gui-Qiang Chen, TaTsien Li and Chun Liu, Contemparay Applied Mathematics, Higher Education Press and World Scientific.
    　

Ⅱ. Chapter in Books

  1. Seiji Ukai, Tong Yang, Stationary Problems of the Boltzmann Equation , Handbook of Differential Equations, Stationary Partial Differential Equations, volume 5, 371-485, Edited by M. Chipot, 2008 Elsevier B.V.. 

　

Ⅲ. Research Papers

v     Conservation Laws

  1. Tong Yang, Huijiang Zhao, Stability of basic wave patterns for gas motions. (To appear)
  2. Zaihong Jiang, Tong Yang, A new nonlinear functional for general scalar hyperbolic conservation laws. (To appear)
  3. Claude Bardos, C. David Levermore, Seiji Ukai, Tong Yang, Kinetic equations and an incompressible fluid dynamical limit that recovers viscous heating, Bulletin of the Institute of Mathematics, Academia Sinica. 3, no. 1, 1-49(2008).
  4. Weike Wang, Tong Yang, Stability of planar diffusion waves for two dimensional Euler equations with damping, Journal of Differential Equations. 242, no. 1, 40-71(2007).
  5. Renjun Duan, Hongxia Liu, Seiji Ukai, Tong Yang, Optimal $L^p$-$L^q$ Convergence rates for the Navier-Stokes equations with potential force, Journal of Differential Equations 238, no. 1, 220-233 (2007).
  6. Renjun Duan, Tong Yang, Changjiang Zhu, Navier-Stokes equations with degenerate viscosity, vacuum and gravitational force, Math. Methods Appl. Sci. 30, no. 3, 347-374 (2007).
  7. Hongxia Liu, Tong Yang A nonlinear functional for general scalar hyperbolic conservation laws, Journal of Differential Equations. 235, no. 2, 658-667 (2007).
  8. Renjun Duan, Seiji Ukai, Tong Yang, Huijiang Zhao, Optimal convergence rates for the compressible Navier-Stokes equations with potential forces, Math. Models Methods Appl. Sci. 17, no. 5, 737-758 (2007).
  9. Chunpeng Wang, Tong Yang, Jingxue Yin, Self-similar solutions and asymptotic behavior for a class of degenerate and singular diffusion equations, Royal Society of Edinburgh Proceeding A. Mathematics 137A, 581-6-2 (2007).
  10. Tong Yang, Mei Zhang, Changjiang Zhu, Existence of strong traveling wave profiles to 2*2 systems of viscous conservation laws, Proceedings of American Mathematical Society  135, no. 6, 1843-1849  (2007).
  11. Yinbin Deng, Tong Yang, Multiplity of stationary solutions to the Euler-Poisson equations, Journal of Differential Equations  231, no. 1, 252-289 (2006).
  12. Jiale Hua, Tong Yang, An improved convergence rate of Glimm scheme for general systems of hyperbolic conservation laws, Journal of Differential Equations 231, no. 1, 92-107 (2006).
  13. Tong Yang, Singular behavior of vacuum states for compressible fluids, Journal of Computational and Applied Mathematics 190, no. 1-2, 211—231 (2006). pdf
  14. Chunpeng Wang, Tong Yang, Jingxue Yin, A Class of Self-Similar Solutions to  a Singular and Degenerate Diffusion Equation, Nonlinear Analysis 60, no. 4, 775-796 (2005). pdf
  15. Tong Yang, Huijiang Zhao, Asymptotics toward Strong Rarefaction Waves for $2\times 2$ Systems of Viscous Conservation Laws, Discrete and Continuous Dynamical Systems. Series A 12, no. 2, 251-282 (2005). pdf
  16. Chaojiang Xu, Tong Yang, Local Existence with Physical Vacuum Boundary Condition to Euler Equations with Damping, Journal of Differential Equations 210, no. 1, 217—231 (2005).
  17. Alberto Bressan, Tong Yang, A Sharp Decay Estimate for Positive Nonlinear Waves, SIAM Journal on Mathematical Analysis 36, no. 2, 659—677 (2004).
  18. Tao Luo, Tong Yang, Global Structure and Asymptotic Behavior of Weak Solutions to Flood Wave Equations, Journal of Differential Equations 207, no. 1, 117—160 (2004).
  19. Tong Yang, Huijiang Zhao, BV Estimates on Lax-Friedrichs' Scheme for a Model of Radiating Gas, Applicable Analysis 83, no. 5, 533—539 (2004).
  20. Alberto Bressan, Tong Yang, On the Convergence Rate of Vanishing Viscosity Approximations, Communications on Pure and Applied Mathematics 57, no. 8, 1075—1109 (2004).
  21. Kenji Nishihara, Tong Yang, Huijiang Zhao, Nonlinear Stability of Strong Rarefaction Waves for Compressible Navier-Stokes Equations. SIAM Journal on Mathematical Analysis 35, no. 6, 1561—1597 (2004). pdf
  22. Yinbin Deng, Jianlin Xiang, Tong Yang, Blowup Phenomena of Solutions to Euler-Poisson Equations, Journal of Mathematical Analysis and Applications 286, no. 1, 295—306 (2003). pdf
  23. Seung-Yeal Ha, Tong Yang, $L\sp 1$ Stability for Systems of Hyperbolic Conservation Laws with a Resonant Moving Source, SIAM Journal on Mathematical Analysis 34, no. 5, 1226--1251 (2003) (electronic).
  24. De-Xing Kong, Tong Yang, Asymptotic Behavior of Global Classical Solutions of Quasilinear Hyperbolic Systems, Communications in Partial Differential Equations 28, no. 5-6, 1203—1220 (2003).
  25. Tong Yang, Changjiang Zhu, Non-existence of Global Smooth Solutions to Symmetrizable Nonlinear Hyperbolic Systems, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 133, no. 3, 719—728 (2003).
  26. Tong Yang, Convergence Rate of Glimm Scheme for General Systems of Hyperbolic Conservation Laws, Taiwanese Journal of Mathematics 7, no. 2, 195—205 (2003). pdf
  27. Weike Wang, Tong Yang, Pointwise Estimates and $L\sb p$ Convergence Rates to Diffusion Waves for $p$-System with Damping, Journal of Differential Equations 187, no. 2, 310—336 (2003).
  28. Tong Yang, Huijiang Zhao, Changjiang Zhu, BV Estimates of Lax-Friedrichs' Scheme for a Class of Nonlinear Hyperbolic Conservation Laws, Proceedings of the American Mathematical Society 131, no. 4, 1257--1266 (2003). pdf
  29. Seak-Weng Vong, Tong Yang, Changjiang Zhu, Compressible Navier-Stokes Equations with Degenerate Viscosity Coefficient and Vacuum. II, Journal of Differential Equations 192, no. 2, 475—501 (2003).
  30. Tai-Ping Liu, Tong Yang, Weak Solutions of General Systems of Hyperbolic Conservation Laws, Communications in Mathematical Physics 230, no. 2, 289—327 (2002). pdf
  31. Yinbin Deng, Tai-Ping Liu, Tong Yang, Zheng-an Yao, Solutions of Euler-Poisson Equations for Gaseous Stars, Archive for Rational Mechanics and Analysis 164, no. 3, 261—285 (2002).
  32. Tong Yang, Changjiang Zhu, Compressible Navier-Stokes Equations with Degenerate Viscosity Coefficient and Vacuum, Communications in Mathematical Physics 230, no. 2, 329—363 (2002).
  33. Tong Yang, Huijiang Zhao, A Vacuum Problem for the One-dimensional Compressible Navier-Stokes Equations with Density-dependent Viscosity, Journal of Differential Equations 184, no. 1, 163—184 (2002). pdf
  34. Tai-Ping Liu, Tong Yang, Yongshu Zheng, Some Nonlinear Functionals for Scalar Conservation Laws, IMS Conference on Differential Equations from Mechanics (Hong Kong, 1999). Methods and Applications of Analysis 8, no. 4, 609—622 (2001).
  35. Tong Yang, Fahuai Yi, Global Existence and Uniqueness for a Hyperbolic System with Free Boundary, Discrete and Continuous Dynamical Systems 7, no. 4, 763—780 (2001).
  36. Weike Wang, Tong Yang, The Pointwise Estimates of Solutions for Euler Equations with Damping in Multi-dimensions, Journal of Differential Equations 173, no. 2, 410—450 (2001).
  37. Ling Hsiao, Tong Yang, Asymptotics of Initial Boundary Value Problems for Hydrodynamic and Drift Diffusion Models for Semiconductors, Journal of Differential Equations 170, no. 2, 472—493 (2001).
  38. Tong Yang, Zheng-an Yao, Changjiang Zhu, Compressible Navier-Stokes Equations with Density-dependent Viscosity and Vacuum, Communications in Partial Differential Equations 26, no. 5-6, 965—981 (2001). pdf
  39.  Tai-Ping Liu, Tong Yang, Compressible Flow with Vacuum and Physical Singularity. Cathleen Morawetz: a Great Mathematician, Methods and Applications of Analysis 7, no. 3, 495—509 (2000).
  40. Tong Yang, Changjiang Zhu, Yongshu Zheng, Existence of Global Smooth Solutions for Euler Equations with Symmetry. II. Nonlinear Analysis 41, no. 1-2, Ser. A: Theory Methods, 187—203 (2000).
  41.  Tong Yang, Huijiang Zhao, Changjiang Zhu, Asymptotic Behavior of Solutions to a Hyperbolic System with Relaxation and Boundary Effect, Journal of Differential Equations 163, no. 2, 348—380 (2000).
  42. Tao Luo, Roberto Natalini, Tong Yang, Global BV Solutions to a $p$-system with Relaxation, Journal of Differential Equations 162, no. 1, 174—198 (2000).
  43. Tong Yang, Changjiang Zhu, Existence and Non-existence of Global Smooth Solutions for $p$-system with Relaxation, Journal of Differential Equations 161, no. 2, 321—336 (2000). pdf
  44. Kenji Nishihara, Weike Wang, Tong Yang, $L\sb p$-convergence Rate to Nonlinear Diffusion Waves for $p$-system with Damping, Journal of Differential Equations 161, no. 1, 191—218 (2000).
  45. Tao Luo, Tong Yang, Interaction of Elementary Waves for Compressible Euler Equations with Frictional Damping, Journal of Differential Equations 161, no. 1, 42—86 (2000).
  46. Tao Luo, Zhouping Xin, Tong Yang, Interface Behavior of Compressible Navier-Stokes Equations with Vacuum, SIAM Journal on Mathematical Analysis 31, no. 6, 1175—1191 (2000). pdf
  47. Tai-Ping Liu, Tong Yang, $L\sb 1$ Stability for Systems of Hyperbolic Conservation Laws, Nonlinear Partial Differential Equations (Evanston, IL, 1998), 183--192, Contemporary Mathematics, 238, American Mathematical Society, Providence, RI, 1999.
  48. Lung-an Ying, Tong Yang, Changjiang Zhu, The Rate of Asymptotic Convergence of Strong Detonations for a Model Problem, Japan Journal of Industrial and Applied Mathematics 16, no. 3, 467—487 (1999).
  49. Alberto Bressan, Tai-Ping Liu, Tong Yang, $L\sp 1$ Stability Estimates for $n\times n$ Conservation Laws, Archive for Rational Mechanics and Analysis 149, no. 1, 1—22 (1999).
  50. Tai-Ping Liu, Tong Yang, $L\sb 1$ Stability of Conservation Laws with Coinciding Hugoniot and Characteristic Curves, Indiana University Mathematics Journal 48, no. 1, 237—247 (1999). pdf
  51. Tai-Ping Liu, Tong Yang, Well-posedness Theory for System of Hyperbolic Conservation Laws, Hyperbolic Problems: Theory, Numerics, Applications, Vol. II (Zürich, 1998), 681-691, International Series of Numerical Mathematics, 130, Birkhäuser, Basel, 1999.
  52. Tai-Ping Liu, Tong Yang, Well-posedness Theory for Hyperbolic Conservation Laws, Communications on Pure and Applied Mathematics 52, no. 12, 1553—1586 (1999). pdf
  53. Kenji Nishihara, Tong Yang, Boundary Effect on Asymptotic Behaviour of Solutions to the $p$-system with Linear Damping,  Journal of Differential Equations 156, no. 2, 439—458 (1999).
  54. Tai-Ping Liu, Tong Yang, A New Entropy Functional for a Scalar Conservation Law, Communications on Pure and Applied Mathematics 52, no. 11, 1427—1442 (1999). pdf
  55. Hailiang Liu, Jinghua Wang, Tong Yang, Nonlinear Stability and Existence of Stationary Discrete Travelling Waves for the Relaxing Schemes, Japan Journal of Industrial and Applied Mathematics 16, no. 2, 195—224 (1999).
  56. Tong Yang, Euler Equations with Spherical Symmetry and an Outing [Outgoing] Absorbing Boundary, Communications in Partial Differential Equations  24, no. 1-2, 1—23 (1999).
  57.  Lung-an Ying, Tong Yang, Changjiang Zhu, Nonlinear Stability of Strong Detonation Waves for a Dissipative Model,  Journal of Differential Equations 151, no. 1, 134—160 (1999).
  58. Tai-Ping Liu, Tong Yang, $L\sb 1$ Stability for $2\times 2$ Systems of Hyperbolic Conservation Laws, Journal of the American Mathematical Society 12, no. 3, 729—774 (1999). pdf
  59. Ming Mei, Tong Yang, Convergence Rates to Travelling Waves for a Nonconvex Relaxation Model, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 128, no. 5, 1053—1068 (1998).
  60. Tao Luo, Tong Yang, Global Weak Solutions for Elastic Equations with Damping and Different End States, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 128, no. 4, 797—807 (1998).
  61. Ling Hsiao, Tao Luo, Tong Yang, Global BV Solutions of Compressible Euler Equations with Spherical Symmetry and Damping,  Journal of Differential Equations 146, no. 1, 203—225 (1998).
  62. Hailiang Liu, Jinghua Wang, Tong Yang, Stability of a Relaxation Model with a Nonconvex Flux, SIAM Journal on Mathematical Analysis 29, no. 1, 18—29 (1998) (electronic).
  63. Tong Yang, Changjiang Zhu, Huijiang Zhao, Compactness Framework of $L\sp p$ Approximate Solutions for Scalar Conservation Laws, Journal of Mathematical Analysis and Applications  220 (1998), no. 1, 164--186.
  64. Tai-Ping Liu, Zhouping Xin, Tong Yang, Vacuum States for Compressible Flow, Discrete and Continuous Dynamical Systems 4, no. 1, 1—32 (1998). pdf
  65. Tong Yang, Zheng-An Yao, Changjiang Zhu, Existence of Global Weak Solutions for a Viscoelastic Model with Relaxation, Applicable Analysis.67, no. 3-4, 313—326 (1997).
  66.  Tong Yang, Changjiang Zhu, Huijiang Zhao, Global Smooth Solutions for a Class of Quasilinear Hyperbolic Systems with Dissipative Terms, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 127, no. 6, 1311—1324 (1997).
  67. Tai-Ping Liu, Tong Yang, Uniform $L\sb 1$ Boundedness of Solutions of Hyperbolic Conservation Laws, Methods and Applications of Analysis 4, no. 3, 339—355 (1997). pdf
  68. Tai-Ping Liu, Tong Yang, Compressible Euler Equations with Vacuum, Journal of Differential Equations 140, no. 2, 223—237 (1997).
  69. Longwei Lin, Hongxia Liu, Tong Yang, Existence of Globally Bounded Continuous Solutions for Nonisentropic Gas Dynamics Equations, Journal of Mathematical Analysis and Applications 209, no. 2, 492—506 (1997).
  70. Lung-an Ying, Tong Yang, Changjiang Zhu, Existence of Global Smooth Solutions for Euler Equations with Symmetry, Communications in Partial Differential Equations 22, no. 7-8, 1361—1387 (1997).
  71. Hailiang Liu, Jinghua Wang, Tong Yang, Existence of the Discrete Travelling Waves for a Relaxing Scheme, Applied Mathematics Letters 10, no. 3, 117—122 (1997).
  72. Hailiang Liu, Ching Wah Woo, Tong Yang, Decay Rate for Travelling Waves of a Relaxation Model, Journal of Differential Equations 134, no. 2, 343—367 (1997).
  73. Tong Yang, A Functional Integral Approach to Shock Wave Solutions of the Euler Equations with Spherical Symmetry. II, Journal of Differential Equations 130, no. 1, 162—178 (1996).
  74. Tong Yang, A Functional Integral Approach to Shock Wave Solutions of Euler Equations with Spherical Symmetry, Communications in Mathematical Physics 171, no. 3, 607—638 (1995).
  75. Long Wei Lin, Tong Yang, Existence and Nonexistence of Global Continuous Solutions to Riemann Problem for Damped $p$-system, Acta Mathematica Scientia. Series B. English Edition  13, no. 1, 1—12 (1993).
  76. Long Wei Lin, Tong Yang, Convergence of the Viscosity Method for the Systems of Isentropic Gas Dynamics in Lagrangian Coordinates, Journal of Differential Equations 102, no. 2, 330—341 (1993).
  77. Long Wei Lin, Tong Yang, Convergence of the Lax-Friedrichs' Scheme for Equations of Isentropic Gas Dynamics in Lagrangian Coordinates, Communications in Partial Differential Equations 16, no. 8-9, 1441—1460 (1991).
  78. Long Wei Lin, Tong Yang, Existence and Nonexistence of Global Smooth Solutions for Damped $p$-system with "Really Large" Initial Data, Journal of Partial Differential Equations 4, no. 2, 45—51 (1991).
  79. Tong Yang, Long Wei Lin, Viscosity method for the $2\times 2$ Quasilinear Hyperbolic Conservation Laws, Journal of Mathematical Research & Exposition. 10, no. 4, 475—484 (1990).

 

v     Boltzmann Equations

  1. Weike Wang, Tong Yang, Xiongfeng Yang, Nonlinear stability of boundary layer solutions to Boltzmann equation for hard potential with angular cut-off. (To appear)
  2. Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang, Regularity of solutions to the spatially homogeneous Boltzmann equation without Angular cutoff. (To appear)
  3. Yoshinori Morimoto, Seiji Ukai, Chaojiang Xu, Tong Yang, Boltzmann equation with Debye-Yukawa potential. (To appear)
  4. Renjun Duan, Seiji Ukai, Tong Yang, Huijiang Zhao, Optimal convergence rates for the Boltzmann equation with potential forces. (To appear)
  5. Seiji Ukai, Tong Yang, Huijiang Zhao, Exterior problem of Boltzmann equation with temperature difference, Communications in Pure and Applied Analysis. 8, no. 1, 479-491(2009).
  6. Seiji Ukai, Tong Yang, Huijiang Zhao, Stationary solutions to the exterior problem for the Boltzmann equation , I. Existence, Discrete and Continuous Dynamical Systems. 23, no. 1-2, 495-520 (2009).
  7. Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang, Uncertainty principle and kinetic equations, Journal of Functional Analysis. 255, no.8, 2013-2066 (2008).
  8. Zhaohui Huo, Yoshinori Morimoto, Seiji Ukai, Tong Yang, Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff, Kinetic and Related Models. 1, no. 3, 453-489(2008).
  9. Renjun Duan, Meng-Rong Li, Tong Yang, Propagation of Singularities in the Solutions to the Boltzmann Equation near Equilibrium, Mathematical Models and Methods in Applied Sciences. 18, no.7, 1093-1114(2008).
  10. Feimin Huang, Zhouping Xin and Tong Yang, Contact discontinuity with general perturbations for gas motions, Advances in Mathematics. 219, no.4, 1246-1297(2008).
  11. Renjun Duan, Seiji Ukai, Tong Yang, Huijiang Zhao, Optimal Decay Estimates on the Linearized Boltzmann Equation with Time Dependent Force and their Applications, Communications in Mathematical Physics, 277, no. 1, (2008).
  12. Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chaojiang Xu, Tong Yang, Uncertainty Principle and Regularity for Boltzmann Type Equations, Comptes rendus Mathemtique. 345, no. 12, 673-677(2007).
  13. Renjun Duan, Tong Yang, Changjiang Zhu, Existence of stationary solutions to the Vlasov-Poisson-Boltzmann system, Journal of  Mathematical Analysis and Applications  327, no. 1, 425-434  (2007).
  14. Weike Wang, Tong Yang, Xiongfeng Yang, Existence of boundary layers to the Boltzmann equation with cutoff soft potentials, Journal of Mathematical Physics, 48, no. 7, 073304, 21pp(2007).
  15. Weike Wang, Tong Yang, Xiongfeng Yang, Nonlinear stability of boundary layers of the Boltzmann equation for cutoff hard potentials, Journal of Mathematical Physics, 47 , no. 8, 083301, 15 pp (2006).
  16. Tong Yang, Huijiang Zhao, global existence of classical solutions to the Vlasov-Poisson-Boltzmann system, Communications in Mathematical Physics 268, no. 3, 569--605 (2006).
  17. Tong Yang, Huijiang Zhao, A new energy method for the Boltzmann equation, Journal of Mathematical Physics 47, no. 5, 053301, 19 pp  (2006).
  18. Seiji Ukai, Tong Yang, The Boltzmann equation in the space $L^2\cap L_\beta^\infty$: Global and time-periodic solutions, Analysis and Applications 4, no. 3, 263-310 (2006).
  19. Renjun Duan, Tong Yang, Changjiang Zhu, L^1 and BV-type stability of the Boltzmann equation with external forces, Journal of Differential Equations  227, no. 1, 1-28 (2006).
  20. Feimin Huang, Tong Yang, Stability of contact discontinuity for the Boltzmann equation, Journal of Differential Equations 229, no. 2, 698-742 (2006).
  21. Tong Yang, Hongjun Yu, Huijiang Zhao, Cauchy problem for the Vlasov-Poisson-Boltzmann system, Archive for Rational Mechanics and Analysis  182, no. 3, 415-470 (2006).
  22. Tai-Ping Liu, Tong Yang, Shih-Hsien Yu, Huijiang Zhao, Nonlinear stability of rarefaction waves for Boltzmann equation, Archive for Rational Mechanics and Analysis, 181, no. 2, 333-371 (2006).
  23. Seiji Ukai, Tong Yang, Huijiang Zhao, Convergence rate to stationary solutions for Boltzmann equation with external force, Chinese Annals of Mathemantics, Ser. B 27, no. 4, 363-378 (2006).
  24. Renjun Duan, Tong Yang, Changjiang Zhu, Boltzmann equation with external force and Vlasov-Poisson-Boltzmann system in infinite vacuum. Discrete and Continuous Dynamical Systems 16, no. 1, 253-277(2006).
  25. Renjun Duan, Tong Yang and Changjiang Zhu, Global Existence to Boltzmann Equation with External Force in Infinite Vacuum, Journal of Mathematical Physics 46, 053307 (2005).
  26. Seiji Ukai, Tong Yang and Huijiang Zhao, Global Solutions to the Boltzmann Equation with External Forces, Analysis and Applications (Singapore) 3, no. 2, 157—193 (2005).
  27. Tong Yang, Huijiang Zhao, A Half-Space Problem for the Boltzmann Equation with Specular Reflection Boundary Condition, Communications in Mathematical Physics 255, no. 3, 683-726 (2005). pdf
  28. Chiun-Chuan Chen, Tai-Ping Liu, Tong Yang, Existence of Boundary Layer Solutions to the Boltzmann Equation, Analysis and Applications (Singapore) 2, no. 4, 337—363 (2004).
  29. Tai-Ping Liu, Tong Yang, Shih-Hsien Yu, Energy Method for Boltzmann Equation, Physica D. Nonlinear Phenomena 188, no. 3-4, 178—192 (2004).
  30. Seiji Ukai, Tong Yang, Shih-Hsien Yu, Nonlinear Stability of Boundary Layers of the Boltzmann Equation. I. The Case $\scr M\sp \infty<-1$, Communications in Mathematical Physics 244, no. 1, 99—109 (2004).
  31. Tai-Ping Liu, Tong Yang, Shih-Hsien Yu, Entropy Pairs for Conservation Laws and $H$-Theorem for the Boltzmann Equation, Lectures on Partial Differential Equations, 167--174, New Studies in Advanced Mathematics, 2, Int. Press, Somerville, MA, (2003).
  32. Seiji Ukai, Tong Yang, Shih-Hsien Yu, Nonlinear Boundary Layers of the Boltzmann Equation. I. Existence, Communications in Mathematical Physics 236, no. 3, 373—393 (2003).

　

Last updated January 09, 2009 by Tong Yang