Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Dong-Ho Tsai"'
Autor:
Dong-Ho Tsai, Xiao-Liu Wang
Publikováno v:
Mathematics in Engineering, Vol 4, Iss 3, Pp 1-14 (2022)
With the help of heat equation, we first construct an example of a graphical solution to the curve shortening flow. This solution $ y\left(x, t\right) \ $has the interesting property that it converges to a log-periodic function of the form $ A\si
Externí odkaz:
https://doaj.org/article/3c04b29568a6463bb5922b17da69fd95
This volume considers the most recent advances in various topics in partial differential equations. Many important issues such as evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completene
Publikováno v:
Journal of Differential Equations. 269:5802-5831
This paper deals with a 1 / κ α -type length-preserving nonlocal flow of convex closed plane curves for all α > 0 . Under this flow, the convexity of the evolving curve is preserved. For a global flow, it is shown that the evolving curve converges
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::19391b60015e34ad4c73b54ff9e8655d
https://doi.org/10.1016/j.jde.2020.04.028
https://doi.org/10.1016/j.jde.2020.04.028
Autor:
Mao-Sheng Chang, Dong-Ho Tsai
Publikováno v:
Journal of Differential Equations. 268:2040-2062
We study the oscillation behavior of solutions to the heat equation on R n and give some interesting examples. We compare the oscillation behavior of the initial data and the oscillation behavior of the solution as t → ∞ .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c7f25744de70be5824afcd961650da93
https://doi.org/10.1016/j.jde.2019.09.021
https://doi.org/10.1016/j.jde.2019.09.021
Autor:
Chia-Hsing Nien, Dong-Ho Tsai
Publikováno v:
Discrete & Continuous Dynamical Systems - A. 40:3997-4017
We look for solutions \begin{document}$ u\left( x,t\right) $\end{document} of the one-dimensional heat equation \begin{document}$ u_{t} = u_{xx} $\end{document} which are space-time periodic, i.e. they satisfy the property \begin{document}$ u\left( x
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8a98a7bd9bcbe06e142940e92d8c0cec
https://doi.org/10.3934/dcds.2020037
https://doi.org/10.3934/dcds.2020037
Publikováno v:
Communications in Analysis and Geometry. 28:1863-1894
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::de00a4c3d6c988a95cc80798012c7d2a
https://doi.org/10.4310/cag.2020.v28.n8.a5
https://doi.org/10.4310/cag.2020.v28.n8.a5
Autor:
Dong-Ho Tsai, Xiao-Liu Wang
Publikováno v:
Acta Mathematica Scientia. 39:1674-1694
We use two simple methods to derive four important explicit graphical solutions of the curve shortening flow in the plane. They are well-known as the circle, hairclip, paperclip, and grim reaper solutions of the curve shortening flow. By the methods,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::769c0e40a77a40d1b679740bdc3bc4db
https://doi.org/10.1007/s10473-019-0616-5
https://doi.org/10.1007/s10473-019-0616-5
Publikováno v:
The Journal of Geometric Analysis. 30:2939-2973
This paper deals with a $$1/\kappa $$-type nonlocal flow for an initial convex closed curve $$\gamma _{0}\subset {\mathbb {R}}^{2}$$ which preserves the convexity and the integral$$\ \int _{X\left( \cdot ,t\right) }\kappa ^{\alpha +1}ds,\ \alpha \in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::06ec474a5396ab6c8965776c40658945
https://doi.org/10.1007/s12220-019-00185-4
https://doi.org/10.1007/s12220-019-00185-4
Autor:
Chia-Hsing Nien, Dong-Ho Tsai
Publikováno v:
Discrete & Continuous Dynamical Systems - A. 39:4073-4089
We study the oscillation behavior of solutions to the one-dimensional heat equation and give some interesting examples. We also demonstrate a simple ODE method to find explicit solutions of the heat equation with certain particular initial conditions
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3323139f9af87f2f230222921bba5ac8
https://doi.org/10.3934/dcds.2019164
https://doi.org/10.3934/dcds.2019164
Autor:
Dong-Ho Tsai, Xiao-Liu Wang
Publikováno v:
SIAM Journal on Mathematical Analysis. 50:1396-1431
We consider long time behavior of a given smooth convex embedded closed curve $\gamma_{0}\subset\mathbb{R}^{2}$ evolving according to a nonlocal curvature flow, which arises in a Hele--Shaw problem and has a prescribed rate of change in its enclosed
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::351c243805805f8af91868831c62770c
https://doi.org/10.1137/17m1125467
https://doi.org/10.1137/17m1125467