Advanced search
Publication Cover
Communications in Partial Differential Equations Volume 24, 1999 - Issue 5-6
Submit an article Journal homepage
37
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A fattening principle for fronts propagating by mean curvature plus a driving force

Yonghoi Koo School of Mathematics, University of Minnesota, Minneapolis, MN 55455 E-mail: [email protected]
Pages 1035-1053 | Published online: 08 May 2007

References

  • Angenent , S. 1991 . On the formation of singularities in the curve shortening pow . J. Diff. Geom. , 33 : 601 – 633 .
  • Angenent , S. , Chopp , D. L. and Ilmanen , T. 1995 . A computed example of nonuniqueness of mean curvature flow in R3 . Comm. Partial Diff. Eq. , 20 : 1937 – 1958 .
  • Barles , G. and Georgelin , C. 1995 . A simple proof of convergence for an approximation scheme for computzng motion by mean curvature . SIAM J. Num. Anal. , 32 : 484 – 500 .
  • Barles , G. , Soner , H. M. and Souganidis , P. E. 1993 . Front propagation and phase field theory . SIAM J. Cont. Optim. , 31 : 439 – 469 .
  • Belletini , G. and Paolini , M. 1994 . Two examples of fattening for the mean curvature flow with a driving force . Atti Accad. Naz. Lincei C1. Sci. Fis. Mat. Natur. Rend. Mat. Appl. , 9 ( 5 ) : 229 – 236 .
  • Brakke , K. A. 1978 . The motion of a surface by its mean curvature , N J : Princeton University Press .
  • Chen , Y. G. , Giga , Y. and Goto , S. 1991 . Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations . J . of Diff. Geom. , 33 : 749 – 786 .
  • Chow , B. and Gulliver , R. Aleksandrov reflection and geometric evolution of hypersurfaces , preprint .
  • Crandall , M. G. and Lions , P. L. 1983 . Viscosity solutions of Hamilton- Jacobi equations . Trans. Amer. Math. Soc. , 277 : 1 – 43 .
  • Crandall , M. G. , Evans , L. C. and Lions , P. L. 1984 . Some properties of viscosity solutions of Hamilton-Jacobi equations . Trans. Amer. Math. Soc. , 282 : 487 – 502 .
  • Crandall , M. G. , Ishii , H. and Lions , P. L. 1992 . User's guide to viscosity solutions of second order partial differential equations . Bull. Amer. Math. Soc. , 27 : 1 – 67 .
  • Evans , L. C. and Spruck , J. 1991 . Motions of level sets by mean curvature I . J. Diff. Geom. , 33 : 635 – 681 .
  • Giga , Y. , Goto , S. , Ishii , H. and Sato , M. H. 1991 . Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains . Indiana Univ. Math. , 40 : 443 – 470 .
  • Ishii , H. and Souganidis , P. 1995 . Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor . Tohoku Math. J . , 47 : 227 – 250 .
  • Ishii , H. 1989 . On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's . Comm. Pure Appl. Math. , 42 : 15 – 45 .
  • Jensen , R. 1988 . The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations . Arch, Rational. Mech. Anal. , 101 : 1 – 27 .
  • Lions , P. L. 1983 . Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations . I Comm. Partial Diff. Eq. , 8 : 1101 – 1134 .
  • Osher , S. and Sethian , J. A. 1988 . Fronts propagating with curvaturedependent speed: algorithms based on Hamilton-Jacobi formulations . J . Comp. Phys. , 79 : 12 – 49 .
  • Protter , M. H. and Weinberger , H. F. 1967 . Maximurn principles in dijferential equations , Prentice Hall .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.