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專任教師

基本資料表

蔡東和 Dong-Ho Tsai
03-571-5131 ext. 33062
dhtsai@math.nthu.edu.tw
03-572-3888
http://www.math.nthu.edu.tw/~dhtsai
蔡東和 Dong-Ho Tsai

教師

偏微分方程、幾何分析
綜三館601室

MathSciNet , Math Genealogy

學校名稱國別系所學位起迄年月
美國明尼蘇達大學數學學院博士1989-09~1996-05
服務機關名稱單位職務期間
國立清華大學數學系教授2004-08~
國立清華大學數學系副教授2003-08~2004-07
美國加州聖地牙哥大學數學系訪問學者2001-03~2001-08
國立中正大學數學系副教授1996-08~2003-07
國立交通大學應用數學系講師1987-08~1988-07
論文名稱
Y.-C. Lin, D.-H. Tsai (2014), Asymptotic behavior of the isoperimetric deficit for expanding convex plane curves, Journal of Evolution Equations, vol. 14, no. 4-5, 779-794, 2014.
C.-C. Poon, D.-H. Tsai (2015), On a nonlinear parabolic equation arising from anisotropic plane curve evolution, Journal of Differential Equations, vol. 258, no. 7, 2375-2407, 2015.
Y.-C. Lin, D.-H. Tsai, X.-L. Wang (2015), On some simple examples of non-parabolic curve flows in the plane, Journal of Evolution Equations, vol. 15, no. 4, 817-845, 2015.
D.-H. Tsai, X.-L. Wang (2015), On length-preserving and area-preserving nonlocal flow of convex closed plane curves, Calculus of Variations & PDEs, vol. 54, 3603-3622, 2015.
L.-Y. Gao, D.-H. Tsai (2016), On a third order flow of convex closed plane curves, Taiwanese Journal of Mathematics, vol. 20, no. 3, 553-567, 2016.
D.-H. Tsai (2018), On flows that preserve parallel curves and their formation of singularities, Journal of Evolution Equations, vol. 18, no. 2, 303-321, 2018.
D.-H. Tsai, X.-L. Wang (2018), The evolution of nonlocal curvature flow arising in a Hele- Shaw problem, SIAM Journal of Mathematical Analysis, vol. 50, no. 1, 1396-1431, 2018.
D.-H. Tsai, C.-H. Nien (2019), On the oscillation behavior of solutions to the one-dimensional heat equation, Discrete & Continuous Dynamical Systems-A, vol. 39, no. 7, 4073-4089, 2019.
D.-H. Tsai, X.-L. Wang (2019), On some simple methods to derive the hairclip and paperclip solutions of the curve shortening flow, published online in September, 2019, Acta Mathematica Scientia, 39B(6), 1674-1694, 2019.
L.-Y. Gao, S.-L. Pan, D.-H. Tsai (2020), Nonlocal flow driven by the radius of curvature with fixed curvature integral, Journal of Geometric Analysis, 30, 2939-2973, 2020.
M.-S. Chang, D.-H. Tsai (2020), On the oscillation behavior of solutions to the heat equation on Rn, published online in September, 2019, Journal of Differential Equations, 268, no. 5, 2040-2062, 2020.
L.-Y. Gao, S.-L. Pan, D.-H. Tsai (2020), On a length-preserving inverse curvature flow of convex closed plane curves, Journal of Differential Equations, 269, no. 7, 5802-5831, 2020.
D.-H. Tsai, C.-H. Nien (2020), On space-time periodic solutions of the one-dimensional heat equation, Discrete & Continuous Dynamical Systems-A, vol. 40, no. 6, 3997-4017, 2020.
N. Sesum, D.-H. Tsai, X.-L. Wang (2020), Evolution of locally convex closed curves in the area-preserving and length-preserving curvature flows, Communications in Analysis and Geometry, vol. 28, no. 8, 1863-1894, 2020.
L.-Y. Gao, S.-L. Pan, D.-H. Tsai (2021), On an area-preserving inverse curvature flow of convex closed plane curves, Journal of Functional Analysis, online publication, 28 pages, January 2021, https://doi.org/10.1016/j.jfa.2021.108931.
D.-H. Tsai (2021), Prescribing oscillation behavior of solutions to the heat equation on R^{n} via the initial data and its average integral, submitted in 2021.
B. Chow, D.-H. Tsai (1996), Geometric expansion of convex plane curves, Journal of Differential Geometry, vol. 44, 312-330, 1996.
B. Chow, L.-P. Liou, D.-H. Tsai (1996), Expansion of embedded curves with turning angle greater than& -兀, Inventiones Mathematicae, 123, 415-429, 1996.
D.-H. Tsai (1996), Geometric expansion of starshaped plane curves, Communications in Analysis and Geometry, vol. 4, no. 3, 459-480, 1996.
B. Chow, L.-P. Liou, D.-H. Tsai (1996), On the nonlinear parabolic equation \partial_{t}u=F(△u+nu) on S^{n}, Communications in Analysis and Geometry, vol. 4, no. 3, 415-434, 1996.
B. Chow, D.-H. Tsai (1997), Expansion of convex hypersurfaces by nonhomogeneous functions of curvature, Asian Journal of Mathematics, vol. 1, no. 4, 769-784, 1997.
B. Chow, D.-H. Tsai (1998), Nonhomogeneous Gauss curvature flows, Indiana University Mathematics journal, vol. 47, no. 3, 965-994, 1998.
D.-H. Tsai (2000), Blowup and convergence of expanding immersed convex plane curves, Communications in Analysis and Geometry, vol. 8, no. 4, 761-794, 2000.
D.-H. Tsai (2002), On the formation of singularities in the curve expanding flow, Calculus of Variations & PDEs, vol. 14, no. 3, 385-398, 2002.
D.-H. Tsai (2003), C^{2,α} estimate of a parabolic Monge-Ampère equation on S^{n}, Proceedings of the American Mathematical Society, vol. 131, no. 10, 3067-3074, 2003.
D.-H. Tsai (2004), Blowup behavior of an equation arising from plane curves expansion, Differential and Integral Equations, vol. 17, no. 7-8, 849-872, 2004.
D.-H. Tsai (2005), Expanding embedded plane curves, Contemporary Mathematics, American Mathematical Society, vol. 367, 189-227, 2005.
D.-H. Tsai (2005), Behavior of the gradient for solutions of parabolic equations on the circle, Calculus of Variations & PDEs, vol. 23, 251-270, 2005.
D.-H. Tsai (2005), Asymptotic closeness to limiting shapes for expanding embedded plane curves, Inventiones Mathematicae, 162, 473-492, 2005.
C.-H. Nien, D.-H. Tsai (2006), Convex curves moving translationally in the plane, Journal of Differential Equations, 225, 605-623, 2006.
Y.-C. Lin, D.-H. Tsai (2008), On a simple maximum principle technique applied to equations on the circle, Journal of Differential Equations, 245, 377-391, 2008.
T.-C. Lin, C.-C. Poon, D.-H. Tsai (2009), Expanding convex immersed closed plane curves, Calculus of Variations & PDEs, 34, 153-178, 2009
Y.-C. Lin, D.-H. Tsai (2009), Evolving a convex closed curve to another one via a length-preserving linear flow, Journal of Differential Equations, 247, 2620-2636, 2009.
Y.-C. Lin, D.-H. Tsai (2010), Using Aleksandrov reflection to estimate the location of the center of expansion, Proceedings of the American Mathematical Society, vol. 138, no. 2, 557-565, 2010.
C.-C. Poon, D.-H. Tsai (2010), Contracting convex immersed closed plane curves, Communications in Analysis and Geometry, vol. 18, no. 1, 23-75, 2010.
Y.-C. Lin, C.-C. Poon, D.-H. Tsai (2012), Contracting convex immersed closed plane curves with slow speed of curvature, Transactions of the AMS, vol. 364, no. 11, 5735-5763, 2012
Y.-C. Lin, D.-H. Tsai (2012), Application of Andrews and Green-Osher inequalities to nonlocal flow of convex plane curves, Journal of Evolution Equations, vol. 12, no. 4, 833-854, 2012.
Y.-C. Lin, D.-H. Tsai (2012), Remarks on some isoperimetric properties of the k - 1 flow, Pacific Journal of Mathematics, vol. 260, no. 1, 197-213, 2012.