General initial data for a class of parabolic equations including the curve shortening problem

Kai-Seng Chou; Ying-Chuen Kwong

doi:10.3934/dcds.2020157

journal article Jan 01, 2020

General initial data for a class of parabolic equations including the curve shortening problem

Discrete and Continuous Dynamical Systems Vol. 40 No. 5 pp. 2963-2986 · American Institute of Mathematical Sciences (AIMS)

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References

26

[1]

Parabolic Equations for Curves on Surfaces Part I. Curves with p-Integrable Curvature

Sigurd Angenent

The Annals of Mathematics 10.2307/1971426

[2]

10.2307/2944327

[3]

[4]

10.1090/s0002-9947-1983-0712265-1

[5]

10.1512/iumj.1984.33.33003

[6]

Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations

Yun Gang Chen, Yoshikazu Giga, Shun'ichi Goto

Journal of Differential Geometry 10.4310/jdg/1214446564

[7]

10.1007/pl00009915

[8]

K. S. Chou and X. P. Zhu, The Curve Shortening Problem, Chapman and Hall/CRC, Boca Raton, FL, 2001. 10.1201/9781420035704

[9]

10.1090/s0894-0347-1988-0928264-9

[10]

E. DiBenedetto, Degenerate Parabolic Equations, Springer-Verlag, New York, 1993. 10.1007/978-1-4612-0895-2

[11]

10.1007/bf00251254

[12]

10.1007/bf01232278

[13]

10.4310/jdg/1214446559

[14]

10.1090/s0002-9947-1992-1068927-8

[15]

10.1007/bf02921385

[16]

A. Friedman, Partial Differential Equations, Holt, Rinehart, Winston, 1969.

[17]

The heat equation shrinking convex plane curves

M. Gage, R. S. Hamilton

Journal of Differential Geometry 10.4310/jdg/1214439902

[18]

10.1016/0022-0396(80)90081-9

[19]

10.3934/dcds.1995.1.449

[20]

The heat equation shrinks embedded plane curves to round points

Matthew A. Grayson

Journal of Differential Geometry 10.4310/jdg/1214441371

[21]

O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, , vol. 23, Translations of Mathematical Monographs, American Mathematical Society, Providence, 1968.

[22]

G. Leoni, A First Course in Sobolev Spaces, American Mathematical Society, Providence, 2009. 10.1090/gsm/105

[23]

10.1007/pl00004604

[24]

10.1090/s0002-9947-1944-0009795-2

[25]

Z. Wu, J. Yin, H. Li and J. Zhao, Nonlinear Diffusion Equations, World Scientific, Singapore, 2001.

[26]

10.1006/jdeq.1995.1132

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Details

Published: Jan 01, 2020
Vol/Issue: 40(5)
Pages: 2963-2986

Authors

Northern Illinois University, DeKalb, IL60115, U.S.A

Cite This Article

Kai-Seng Chou, Ying-Chuen Kwong (2020). General initial data for a class of parabolic equations including the curve shortening problem. Discrete and Continuous Dynamical Systems, 40(5), 2963-2986. https://doi.org/10.3934/dcds.2020157

General initial data for a class of parabolic equations including the curve shortening problem

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