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Academic Staff

Yu, Shih-Hsien

Yu, Shih-Hsien

Distinguished Research Fellow

Research Fields: Kinetic equations, Viscous conservation laws, Finite difference equations,

Email : matysh@gate.sinica.edu.tw

Extension : 737

  • Ph.D. in Mathematics Stanford University 1994
  • M.S. in Mathematics National Taiwan University 1989
  • B.S. in Mathematics National Taiwan University 1986

  • Distinguished Research Fellow Institute of Mathematics, Academia Sinica 2021 -
  • Joint Appointment Professor National Yang Ming Chiao Tung University 2022 -
  • Joint Appointment Professor National Taiwan University 2022 -
  • Provost Chair Professor National Univ. of Singapore 2013 - 2016
  • Professor National Univ. of Singapore 2007-2022
  • 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

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

  • (with C.-H. Cheng, T.-P. Liu, and S.-H. Yu) "Green's function of heat equation for heterogeneous media in 3-D", Communications in Partial Differential Equations, 47 (11), 2180-2216, 2022
  • (with H. Wang, S.-H. Yu, and X. Zhang) "Global well-posedness of compressible Navier-Stokes equation with BV∩L1 initial data", Archive for Rational Mechanics and Analysis, 245 (1), 375-477, 2022
  • (with Liu Tai-Ping) "Navier-Stokes Equations in Gas Dynamics: Green's function, singularity, and well-posedness.", Communications on Pure and Applied Mathematics, 75 (2), 223-348, 2022, Link
  • (with Liu Tai-Ping) "Multi-dimensional wave propagation over a Burgers shock profile.", Arch. Ration. Mech. Anal., 229 (1), 231-337, 2018
  • (with Deng Shijin) "Green's function and pointwise convergence for compressible Navier-Stokes equations.", Quart. Appl. Math., 75 (3), 433-503, 2017
  • (with Deng Shijin, Wang Weike) "Green's functions of wave equations in $R_nxR_+$.", 216 (3), 881-903, 2015
  • (with Liu Tai-Ping) "Boundary wave propagator for compressible Navier-Stokes equations.", Found. Comput. Math., 14 (6), 1287-1335, 2014
  • (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
  • (with Liu Tai-Ping) "Fujita equation with boundary effect.", Bull. Inst. Math. Acad. Sin. (N.S.), 9 (2), 267-282, 2014
  • "Initial and shock layers for Boltzmann equation.", Arch. Ration. Mech. Anal., 211 (1), 1-60, 2014
  • (with Wang Haitao) "Algebraic-complex scheme for Dirichlet-Neumann data for parabolic system.", Arch. Ration. Mech. Anal., 211 (3), 1013-1026, 2014
  • (with Deng Shijin, Du Linglong) "Nonlinear stability of Broadwell model with Maxwell diffuse boundary condition.", Kinet. Relat. Models, 6 (4), 865-882, 2013
  • (with Liu Tai-Ping) "Invariant manifolds for steady Boltzmann flows and applications.", Arch. Ration. Mech. Anal., 209 (3), 869-997, 2013
  • (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
  • (with Deng Shijin, Wang Weike) "Viscous conservation laws with boundary.", SIAM J. Math. Anal., 44 (4), 2695-2755, 2012
  • (with Liu Tai-Ping) "On boundary relation for some dissipative systems.", Bull. Inst. Math. Acad. Sin. (N.S.), 6 (3), 245-267, 2011
  • (with Liu Tai-Ping) "Solving Boltzmann equation, Part I: Green's function.", Bull. Inst. Math. Acad. Sin. (N.S.), 6 (2), 115-243, 2011
  • (with Deng Shijin, Wang Weike) "Broadwell model and conservative supersonic boundary.", Arch. Ration. Mech. Anal., 200 (1), 203-223, 2011
  • (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
  • (with Liu Tai-Ping) "Viscous rarefaction waves.", Bull. Inst. Math. Acad. Sin. (N.S.), 5 (2), 123-179, 2010
  • "Nonlinear wave propagations over a Boltzmann shock profile.", J. Amer. Math. Soc., 23 (4), 1041-1118, 2010
  • (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
  • "Stochastic formulation for the initial- boundary value problems of the Boltzmann equation.", Arch. Ration. Mech. Anal., 192 (2), 217-274, 2009
  • (with Liu Tai-Ping) "Boltzmann equation, boundary effects.", Discrete Contin. Dyn. Syst., 24 (1), 145-157, 2009
  • (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
  • (with Lan Chiu-Ya, Lin Huey-Er) "The Green's function for the Broadwell model with a transonic boundary. ", J. Hyperbolic Differ, 0 (2), 279-294, 2008
  • (with Deng Shijin, Wang Weike) "Pointwise convergence to Knudsen layers of the Boltzmann equation.", Comm. Math. Phys., 281 (2), 287-347, 2008
  • (with Liu Tai-Ping) "Diffusion under gravitational and boundary effects.", Bull. Inst. Math. Acad. Sin. (N.S.), 3 (1), 167-210, 2008
  • (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
  • (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
  • (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
  • (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
  • (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
  • "The development of the Green's function for the Boltzmann equation.", J. Stat. Phys., 124 (2月4日), 301-320, 2006
  • (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
  • (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
  • (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
  • "Hydrodynamic limits with shock waves of the Boltzmann equation.", Comm. Pure Appl. Math., 58 (3), 409-443, 2005
  • (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
  • (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
  • (with Liu Tai-Ping) "Boltzmann equation: micro- macro decompositions and positivity of shock profiles.", Comm. Math. Phys., 264 (1), 133-179, 2004
  • (with Liu Tai-Ping, Yang Tong) "Energy method for Boltzmann equation.", Phys. D, 188 (3月4日), 178-192, 2004
  • (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
  • (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
  • (with Ukai Seiji, Tang Tong) "Nonlinear boundary layers of the Boltzmann equation.", Hyperbolic problems: theory, numerics, applications, 103-110, 2003
  • (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
  • "Small divisor and discrete shock profile. Mathematical analysis of liquids and gases (Japanese) (Kyoto, 1999).", Sūrikaisekikenkyūsho Kōkyūroku, 1146, 198-208, 2000
  • (with Liu Tai-Ping) "Hyperbolic conservation laws and dynamic systems.", Discrete Contin. Dynam. Systems, 6 (1), 143-145, 2000
  • "Zero-dissipation limit of solutions with shocks for systems of hyperbolic conservation laws.", Arch. Ration. Mech. Anal., 146 (4), 275-370, 1999
  • (with Liu Tai-Ping) "Nonlinear stability of weak detonation waves for a combustion model.", Comm. Math. Phys., 204 (3), 551-586, 1999
  • (with Liu Tai-Ping) "Continuum shock profiles for discrete conservation laws. II. Stability. ", Comm. Pure Appl. Math., 52 (9), 1047-1073, 1999
  • (with Liu Tai-Ping) "Continuum shock profiles for discrete conservation laws. I. Construction.", Comm. Pure Appl. Math., 52 (1), 85-127, 1999
  • (with Jiang Guang-Shan) "Discrete shocks for finite difference approximations to scalar conservation laws.", SIAM J. Numer. Anal., 35 (2), 749-772, 1998
  • (with Smyrlis, Yiorgos Sokratis) "Existence and stability of traveling discrete shocks.", Numerical analysis and its applications (Rousse, 1996),, 1196, 466-473, 1997
  • (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
  • (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
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