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Academic Staff

Hui, Kin Ming

Hui, Kin Ming

Research Fellow

Research Fields: Partial Differential Equations, , Geometric Analysis, Applied Mathematics

Email : kmhui@gate.sinica.edu.tw

Extension : 707

  • Ph.D., University of Chicago,1990
  • M.S. , University of Chicago, 1986
  • B.S., University of Hong Kong, 1984

  • Applied Mathematics
  • Geometric Analysis
  • Partial Differential Equations

  • Partial differential equations

  • Researcher

  • Lecturer in Mathematics University of Chicago 1987 - 1989
  • Assistant Research Fellow Institute of Mathematics, Academia Sinica 1990/10 - 1993/9
  • Associate Research Fellow Institute of Mathematics, Academia Sinica 1993/10 - 1999/7
  • Research Fellow Institute of Mathematics, Academia Sinica 1999 - Present

  • 1997, Receipent of the travel grant of the Taipei Trade Centre Exchange Scheme to visit the Department of Mathematics of the University of Hong Kong
  • 1994, Recipient of Travel Grants for Young Mathematicians for the International Congress of Mathematicians held in Zurich,

  • "K.M. Hui, Global behaviour of solutions of the lubrication equation with porous medium Van der Waals interactions", (in preparation), preprint
  • "K.M. Hui, Global behaviour of solution of a nonlinear fourth order parabolic equation", (in preparation), preprint
  • "Existence and uniqueness of the singular self-similar solutions of the fast diffusion equation and logarithmic diffusion equation", 2024, Link
  • "Existence of singular rotationally symmetric gradient Ricci solitons in higher dimensions", Canadian Math. Bulletin, 2024, http://dx.doi.org/10.4153/S0008439524000237, Link, Link
  • (with Kai-Seng Chou) "Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem", Journal of Mathematical Analysis and Applicaitons, 532 (2), 2024, https://doi.org/10.1016/j.jmaa.2023.127929, Link, Link
  • (with Soojung Kim) "Vanishing time behavior of solutions to the fast diffusion equation", Communications in Analysis and Geometry, 31 (2), 2023, https://www.intlpress.com/site/pub/files/_fulltext/journals/cag/2023/0031/0002/CAG-2023-0031-0002-a001.pdf, Link, Link
  • "Existence of hypercylinder expanders of the inverse mean curvature flow", Canadian Math. Bulletin, 65 (3), 543-551, 2022, Link
  • (with Jinwan Park) "Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured Euclidean space", Discrete and Continuous Dynamical Systems , 41 (11), 5473-5508, 2021 , Link
  • "Uniqueness and time oscillating behaviour of finite points blow-up solutions of the fast diffusion equation", Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 150 (6), 2849-2870, 2020 , Link
  • (with Sunghoon Kim) "Singular limit of the generalized Burgers equation with absorption ", Journal of Dynamics and Differential Equations, 32, 809-822, 2020, Link
  • (with Sunghoon Kim) "Singular limits and properties of solutions of some degenerate elliptic and parabolic equations", Proceedings of the Royal Society of Edinburgh Section A Mathematics, 149 (2), 353-385, 2019-04 , Link
  • "K.M. Hui, Existence of self-similar solution of the inverse mean curvature flow", Discrete and Continuous Dynamical Systems--Series A , 39 (2), 863-890, 2019, Link
  • (with Sunghoon Kim) "Existence and large time behaviour of finite points blow-up solutions of the fast diffusion equation", Calculus of Variations and PDE, https://doi.org/10.1007/s00526-018-1396-9, 57 (5), 2018-10 , Link, Link
  • (with Soojung Kim) "Asymptotic large time behavior of singular solutions of the fast diffusion equation ", Discrete and continuous dynamical systems Series A , 37 (11), 5943-5977, 2017-11 , Link
  • "K.M. Hui, Asymptotic behaviour of solutions of the fast diffusion equation near its extinction time ", J. Math. Anal. and Appl. , 454 (2), 695-715, 2017-10 , Link
  • (with Sunghoon Kim) "Existence of Neumann and singular solutions of the fast diffusion equation", Discrete and Contin. Dynamical Systems-Series A, 35 (10), 4859-4887, 2015-10 , Link
  • (with Sunghoon Kim) "Decay rate and radial symmetry of the exponential elliptic equation", J. Math. Anal. Appl., 413, 269-283, 2014, Link
  • (with Sunghoon Kim) "Extinction profile of the logarithmic diffusion equation", Manuscripta Mathematica, 143 (3月4日), 491-524, 2014, Link
  • (with Sunghoon Kim) "Large time behaviour of higher dimensional logarithmic diffusion equation", Proceedings of the Royal Society of Edinburgh A, 143, 817-830, 2013, Link
  • "K.M. Hui, Collapsing behaviour of a singular diffusion equation", Discrete and Continuous Dynamical Systems-Series A, 32 (6), 2165-2185, 2012, Link
  • (with Sunghoon Kim) "Convergence of the Dirichlet solutions of the very fast diffusion equation", Nonlinear Analysis, Theory, Methods and Applications , 74 (18), 7404-7425, 2011, Link
  • "K.M. Hui, Quenching behaviour of a nonlocal parabolic MEMS equation", Advances in Mathematical Sciences and Applications, 21 (1), 173-185, 2011
  • "K.M. Hui, Existence and dynamic properties of a nonlocal MEMS equation", Nonlinear Analysis, TMA, 74, 298-316, 2011, Link
  • "K.M. Hui, Another proof for the removable singularities of the heat equation", Proceedings Amer. Math. Soc. , 138 (7), 2397-2402, 2010, Link
  • "K.M. Hui, Growth rate and extinction rate of a reaction-diffusioin equation with a singular nonlinearity", Differential and Integral Equations , 22 (7月8日), 771-786, 2009, Link
  • "K.M. Hui, Global and touchdown behaviour of the generalized MEMS device equation ", Advances in Mathematical Sciences and Applications, 19 (1), 1-25, 2009
  • "K.M. Hui, Singular limit of solutions of the very fast diffusion equation", Nonlinear Analysis, TMA, 68 (5), 1120-1147, 2008, Link
  • "K.M. Hui, Existence of solutions of the very fast diffusion equation in bounded and unbounded domain", Mathematische Annalen, 339 (2), 395-443, 2007
  • "K.M.Hui, Large time behaviour of solutions of a degenerate fourth order parabolic equation, ", Advances in Mathematical Sciences and Applications , 16 (2), 467-478, 2006
  • "K.M.Hui, Existence of solutions of the very fast diffusion equation", Nonlinear Analysis TMA , 58, 75-100, 2004
  • "K.M. Hui, On some Dirichlet and Cauchy problems for a singular diffusion equation", Differential and Integral Equations , 15 (7), 769-804, 2002
  • "K.M. Hui, Asymptotic behaviour of solutions of $u_t=\Delta\log u$ in a bounded domain", Differential and Integral Equations, 14 (2), 175-188, 2001
  • "K.M. Hui, Existence of solutions of the equation $u_t=\Delta\log u$", Nonlinear Analysis TMA , 37, 875-914, 1999
  • "K.M. Hui, Singular limit of solutions of the equation $u_t=\Delta(u^m/m)$ as $m\to 0$", Pacific J. Math. , 187 (2), 297-316, 1999
  • "K.M. Hui, Singular limit of solutions of the porous medium equation with absorption ", Trans. Amer. Math. Soc., 350 (11), 4651-4667, 1998
  • "K.M. Hui, Asymptotic behaviour of solutions of the modified lubrication equation", Applicable Analysis, 62, 311-321, 1996, Link
  • "K.M.Hui, Singular limit of solutions of some degenerate parabolic equations", Nonlinear waves (Sapporo), GAKUTO Internat. Ser. Math. Sci. Appl., 10, 161-162, 1995
  • "K.M. Hui, Singular limit of solutions $u_t=\Delta u^m-A\cdot\nabla (u^q/q)$ as $q\to\infty$ ", Trans. Amer. Math. Soc. , 347 (5), 1687-1712, 1995
  • "K.M. Hui, Singular limit of solutions of the generalized p-Laplacian equation ", Nonlinear Analysis TMA , 24 (9), 1327-1345, 1995
  • "K.M. Hui, Non-existence of fundamental solutions of the equation $u_t=\Delta log u$", J. Math. Anal. and Appl., 182, 800-809, 1994
  • "K.M. Hui, Fatou theorem for the solutions of some nonlinear equations", J. Math. Analy. and Appl. , 183 (1), 37-52, 1994
  • "K.M. Hui, Asymptotic behaviour of solutions of $u_t=\Delta u^m-u^p$ as $p\to\infty$ ", Nonlinear Analysis TMA , 21, 191-195, 1993
  • "K.M. Hui, Nonnegative solutions of the fast diffusion equation with strong reaction ", Nonlinear analysis TMA, 19, 1155-1178, 1992, Link
  • "K.M. Hui, Comparsion theorems for the eigenvalues of the Laplacian in the unit ball in $R^n$", Canad. Math. Bull., 35, 214-217, 1992
  • "K.M. Hui, A Fatou theorem for the solution of the heat equation at the corner points of a cylinder ", Trans. Amer. Math. Soc., 333, 607-642, 1992
  • "K.M. Hui, Global behaviour of solutions of the lubrication equation with porous medium Van der Waals interactions", (preprint), (in preparation)
  • "K.M. Hui, Global behaviour of solution of a nonlinear fourth order parabolic equation", (preprint), (in preparation)
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