研究員 | 許健明
聯絡資訊
- kmhui$\color{red}{@}$gate.sinica.edu.tw
- +886 2 2368-5999 ext. 707
- +886 2 2368-9771
- 偏微分方程
- 幾何分析
- 應用數學
- Ph.D. 美國芝加哥大學 (1990)
- M.S. 美國芝加哥大學 (1986)
- B.S. 香港大學 (1984)
相關連結
經歷
- Research Fellow Institute of Mathematics, Academia Sinica 1999 - Present
- Associate Research Fellow Institute of Mathematics, Academia Sinica 1993/10 - 1999/7
- Assistant Research Fellow Institute of Mathematics, Academia Sinica 1990/10 - 1993/9
- Lecturer in Mathematics University of Chicago 1987 - 1989
獲獎
- Keynote speaker of Symposium on Applied Mathematics and Data Science 2023, 2023-07
- Receipent of the travel grant of the Taipei Trade Centre Exchange Scheme to visit the Department of Mathematics of the University of Hong Kong, 1997
- Recipient of Travel Grants for Young Mathematicians for the International Congress of Mathematicians held in Zurich, 1994
研究簡介
偏微分方程、應用數學、幾何分析
部分著作目錄
- "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.
- "K.M. Hui, Existence and uniqueness of the singular self-similar solutions of the fast diffusion equation and logarithmic diffusion equation" , (preprint) , 2023-12. (https://arxiv.org/abs/2308.10221)
- "K.M. Hui, Existence of singular rotationally symmetric gradient Ricci solitons in higher dimensions" , (preprint) , 2023-12. (https://arxiv.org/abs/2107.13685)
- (with Kai-Seng Chou) "Nonnegative solutions of the heat equation in a cylindrical domain and Widder's theorem" , (accepted for publication by the Journal of Mathematical Analysis and Applicaitons) https://doi.org/10.1016/j.jmaa , 532 (2), 127929-, 2023-11. (https://arxiv.org/abs/2210.10954)
- (with Soojung Kim) "Vanishing time behavior of solutions to the fast diffusion equation" , Communications in Analysis and Geometry , 31 (2), 243-290, 2023. (https://arxiv.org/abs/1811.04410)
- "K.M. Hui, Existence of hypercylinder expanders of the inverse mean curvature flow" , Canadian Math. Bulletin , 65 (3), 543-551, 2022.
- (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, 2021-11.
- "K.M. Hui, 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, 2020-12.
- (with Sunghoon Kim) "Singular limit of the generalized Burgers equation with absorption" , Journal of Dynamics and Differential Equations , 32, 809-822, 2020.
- (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.
- "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.
- (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. (article 112)
- (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.
- "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.
- (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.
- (with Sunghoon Kim) "Decay rate and radial symmetry of the exponential elliptic equation" , J. Math. Anal. Appl. , 413, 269-283, 2014.
- (with Sunghoon Kim) "Extinction profile of the logarithmic diffusion equation" , Manuscripta Mathematica , 143 (3-4), 491-524, 2014.
- (with Sunghoon Kim) "Large time behaviour of higher dimensional logarithmic diffusion equation" , Proceedings of the Royal Society of Edinburgh A , 143, 817-830, 2013.
- "K.M. Hui, Collapsing behaviour of a singular diffusion equation" , Discrete and Continuous Dynamical Systems-Series A , 32 (6), 2165-2185, 2012.
- (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.
- "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.
- "K.M. Hui, Another proof for the removable singularities of the heat equation" , Proceedings Amer. Math. Soc. , 138 (7), 2397-2402, 2010.
- "K.M. Hui, Growth rate and extinction rate of a reaction-diffusioin equation with a singular nonlinearity" , Differential and Integral Equations , 22 (7-8), 771-786, 2009.
- "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.
- "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.
- "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.
- "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.
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