Distinguished Research Fellow |   Yu, Shih-Hsien
Contact Information
  • matysh$\color{red}{@}$gate.sinica.edu.tw
  • +886 2 2368-5999 ext. 737
  • +886 2 2368-9771
Research Interests
  • Kinetic equations
  • Viscous conservation laws
  • Finite difference equations
Education
  • Ph.D. in Mathematics Stanford University (1994)
  • M.S. in Mathematics National Taiwan University (1989)
  • B.S. in Mathematics National Taiwan University (1986)

Work Experience
  • Provost Chair Professor National Univ. of Singapore 2013 - 2016
  • Professor National Univ. of Singapore 2007-present
  • Associate Professor City Univ. of Hong Kong 2000 - 2007
  • Associate Professor Osaka Univ. 1999 - 2000
  • CAM Assistant Professor Univ. of California, LA 1995 - 1999
  • Postdoctoral researcher Univ. of Minnesota 1994 - 1995

Awards
  • Invited speaker, International Congress of Mathematics, Seoul, Korea, 2014
  • Provost Chair Professor, National University of Singapore, 2013 - 2016
  • Outstanding Scientist Award, National University of Singapore, 2010

Research Descriptions


Selected Publications
  1. (with Liu Tai-Ping) "Navier-Stokes Equations in Gas Dynamics: Green's function, singularity, and well-posedness." , Preprint..
  2. (with Liu Tai-Ping) "Multi-dimensional wave propagation over a Burgers shock profile." , Arch. Ration. Mech. Anal. , 229 (1), 231-337, 2018.
  3. (with Deng Shijin) "Green's function and pointwise convergence for compressible Navier-Stokes equations." , Quart. Appl. Math. , 75 (3), 433-503, 2017.
  4. (with Deng Shijin, Wang Weike) "Green's functions of wave equations in $R_nxR_+$." , 216 (3), 881-903, 2015.
  5. (with Liu Tai-Ping) "Boundary wave propagator for compressible Navier-Stokes equations." , Found. Comput. Math. , 14 (6), 1287-1335, 2014.
  6. (with Deng Shijin, Wang Weike) "Bifurcation on boundary data for linear Broadwell model with conservative boundary condition." , J. Hyperbolic Differ. Equ. , 11 (3), 603-619, 2014.
  7. (with Liu Tai-Ping) "Fujita equation with boundary effect." , Bull. Inst. Math. Acad. Sin. (N.S.) , 9 (2), 267-282, 2014.
  8. "Initial and shock layers for Boltzmann equation." , Arch. Ration. Mech. Anal. , 211 (1), 1-60, 2014.
  9. (with Wang Haitao) "Algebraic-complex scheme for Dirichlet-Neumann data for parabolic system." , Arch. Ration. Mech. Anal. , 211 (3), 1013-1026, 2014.
  10. (with Deng Shijin, Du Linglong) "Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition." , Kinet. Relat. Models , 6 (4), 865-882, 2013.
  11. (with Liu Tai-Ping) "Invariant manifolds for steady Boltzmann flows and applications." , Arch. Ration. Mech. Anal. , 209 (3), 869-997, 2013.
  12. (with Liu Tai-Ping) "Dirichlet-Neumann kernel for hyperbolic-dissipative system in half-space." , Bull. Inst. Math. Acad. Sin. (N.S.) , 7 (4), 477-543, 2012.
  13. (with Deng Shijin, Wang Weike) "Viscous conservation laws with boundary." , SIAM J. Math. Anal. , 44 (4), 2695-2755, 2012.
  14. (with Liu Tai-Ping) "On boundary relation for some dissipative systems." , Bull. Inst. Math. Acad. Sin. (N.S.) , 6 (3), 245-267, 2011.
  15. (with Liu Tai-Ping) "Solving Boltzmann equation, Part I: Green's function." , Bull. Inst. Math. Acad. Sin. (N.S.) , 6 (2), 115-243, 2011.
  16. (with Deng Shijin, Wang Weike) "Broadwell model and conservative supersonic boundary." , Arch. Ration. Mech. Anal. , 200 (1), 203-223, 2011.
  17. (with Liu Tai-Ping, Zeng Yanni) "Viscous conservation laws, Part I: scalar laws." , Bull. Inst. Math. Acad. Sin. (N.S.) , 5 (3), 233-310, 2010.
  18. (with Liu Tai-Ping) "Viscous rarefaction waves." , Bull. Inst. Math. Acad. Sin. (N.S.) , 5 (2), 123-179, 2010.
  19. "Nonlinear wave propagations over a Boltzmann shock profile." , J. Amer. Math. Soc. , 23 (4), 1041-1118, 2010.
  20. (with Liu Tai-Ping) "Viscous shock wave tracing, local conservation laws, and pointwise estimates." , Bull. Inst. Math. Acad. Sin. (N.S.) , 4 (3), 235-297, 2009.
  21. "Stochastic formulation for the initial- boundary value problems of the Boltzmann equation." , Arch. Ration. Mech. Anal. , 192 (2), 217-274, 2009.
  22. (with Liu Tai-Ping) "Boltzmann equation, boundary effects." , Discrete Contin. Dyn. Syst. , 24 (1), 145-157, 2009.
  23. (with Lien Wen-Ching) "Time-asymptotic interactions of Boltzmann shock layers in the presence of boundary." , Indiana Univ. Math. J. , 57 (4), 1501-1556, 2008.
  24. (with Lan Chiu-Ya, Lin Huey-Er) "The Green's function for the Broadwell model with a transonic boundary." , J. Hyperbolic Differ , Equ. 5 (2), 279-294, 2008.
  25. (with Deng Shijin, Wang Weike) "Pointwise convergence to Knudsen layers of the Boltzmann equation." , Comm. Math. Phys. , 281 (2), 287-347, 2008.
  26. (with Liu Tai-Ping) "Diffusion under gravitational and boundary effects." , Bull. Inst. Math. Acad. Sin. (N.S.) , 3 (1), 167-210, 2008.
  27. (with Aoki Kazuo, Golse François, Liu, Tai-Ping) "Preface [Special issue in honor of the seventieth birthday of Yoshio Sone]." , Bull. Inst. Math. Acad. Sin. (N.S.) , 3 (1), 2008.
  28. (with Deng Shijin, Wang Weike) "Pointwise convergence of the boundary layer of the Boltzmann equation for the cutoff hard potential." , 14 (4), 307-344, 2007.
  29. (with Deng Shijin, Wang Weike) "Pointwise convergence to a Maxwellian for a Broadwell model with a supersonic boundary." , Netw. Heterog. Media , 2 (3), 383-395, 2007.
  30. (with Liu Tai-Ping) "Initial-boundary value problem for one-dimensional wave solutions of the Boltzmann equation." , Comm. Pure Appl. Math. , 60 (3), 295-356, 2007.
  31. (with Lee Ming-Yi, Liu Tai-Ping) "Large-time behavior of solutions for the Boltzmann equation with hard potentials." , Comm. Math. Phys. , 269 (1), 17-37, 2007.
  32. "The development of the Green's function for the Boltzmann equation." , J. Stat. Phys. , 124 (2-4), 301-320, 2006.
  33. (with Liu Tai-Ping) "Green's function of Boltzmann equation, 3-D waves." , Bull. Inst. Math. Acad. Sin. (N.S.) , 1 (1), 1-78, 2006.
  34. (with Liu Tai-Ping, Yang Tong, Zhao Hui-Jiang) "Nonlinear stability of rarefaction waves for the Boltzmann equation." , Arch. Ration. Mech. Anal. , 181 (2), 333-371, 2006.
  35. (with Lan Chiu-Ya, Lin Huey-Er) "The Green's functions for the Broadwell model in a half space problem." , Netw. Heterog. Media , 1 (1), 167-183, 2006.
  36. "Hydrodynamic limits with shock waves of the Boltzmann equation." , Comm. Pure Appl. Math. , 58 (3), 409-443, 2005.
  37. (with Lan Chiu-Ya, Lin Huey-Er, Liu Tai-Ping) "Propagation of viscous shock waves away from the boundary." , SIAM J. Math. Anal. , 36 (2), 580-617, 2004.
  38. (with Liu Tai-Ping) "The Green's function and large-time behavior of solutions for the one-dimensional Boltzmann equation." , Comm. Pure Appl. Math. , 57 (12), 1543-1608, 2004.
  39. (with Liu Tai-Ping) "Boltzmann equation: micro- macro decompositions and positivity of shock profiles." , Comm. Math. Phys. , 264 (1), 133-179, 2004.
  40. (with Liu Tai-Ping, Yang Tong) "Energy method for Boltzmann equation." , Phys. D , 188 (3-4), 178-192, 2004.
  41. (with Ukai Seiji, Yang Tong) "Nonlinear stability of boundary layers of the Boltzmann equation. I. The case $M_\infty<-1$" , Comm. Math. Phys. , 244 (1), 99-109, 2004.
  42. (with Liu Tai-Ping, Yang Tong) "Entropy pairs for conservation laws and H-theorem for the Boltzmann equation." , Lectures on partial differential equations , 167-174, 2003.
  43. (with Ukai Seiji, Tang Tong) "Nonlinear boundary layers of the Boltzmann equation." , Hyperbolic problems: theory, numerics, applications , 103-110, 2003.
  44. (with Ukai Seiji, Tang Tong) "Nonlinear boundary layers of the Boltzmann equation. Mathematical analysis in fluid and gas dynamics (Japanese) (Kyoto, 2001)." , Sūrikaisekikenkyūsho Kōkyūroku , 1247, 208-215, 2002.
  45. "Small divisor and discrete shock profile. Mathematical analysis of liquids and gases (Japanese) (Kyoto, 1999)." , Sūrikaisekikenkyūsho Kōkyūroku , 1146, 198-208, 2000.
  46. (with Liu Tai-Ping) "Hyperbolic conservation laws and dynamic systems." , Discrete Contin. Dynam. Systems , 6 (1), 143-145, 2000.
  47. "Zero-dissipation limit of solutions with shocks for systems of hyperbolic conservation laws." , Arch. Ration. Mech. Anal. , 146 (4), 275-370, 1999.
  48. (with Liu Tai-Ping) "Nonlinear stability of weak detonation waves for a combustion model." , Comm. Math. Phys. , 204 (3), 551-586, 1999.
  49. (with Liu Tai-Ping) "Continuum shock profiles for discrete conservation laws. II. Stability." , Comm. Pure Appl. Math. , 52 (9), 1047-1073, 1999.
  50. (with Liu Tai-Ping) "Continuum shock profiles for discrete conservation laws. I. Construction." , Comm. Pure Appl. Math. , 52 (1), 85-127, 1999.
  51. (with Jiang Guang-Shan) "Discrete shocks for finite difference approximations to scalar conservation laws." , SIAM J. Numer. Anal. , 35 (2), 749-772, 1998.
  52. (with Smyrlis, Yiorgos Sokratis) "Existence and stability of traveling discrete shocks." , Numerical analysis and its applications (Rousse, 1996), , 1196, 466-473, 1997.
  53. (with Liu Tai-Ping) "Propagation of a stationary shock layer in the presence of a boundary." , Arch. Rational Mech. Anal. , 139 (1), 57-82, 1997.
  54. (with Nishibata Shinya) "The asymptotic behavior of the hyperbolic conservation laws with relaxation on the quarter-plane." , SIAM J. Math. Anal. , 28 (2), 304-321, 1997.