On the evolution of curves via a function of curvature. I. The classical case
作者： Benjamin B Kimia , Allen Tannenbaum , Steven W Zucker
DOI: 10.1016/0022-247X(92)90260-K
关键词:
摘要: Abstract The problem of curve evolution as a function its local geometry arises naturally in many physical applications. A special case this is the shortening which has been extensively studied. Here, we consider general and prove an existence theorem for classical solution. main rests on lemmas that bound length, curvature, how far can travel.
elsevier.com
sci-hub.se 参考文章(12)
PETER LAX, Shock Waves and Entropy Contributions to Nonlinear Functional Analysis#R##N#Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, April 12–14, 1971. pp. 603- 634 ,(1971) , 10.1016/B978-0-12-775850-3.50018-2
Matthew A. Grayson, The heat equation shrinks embedded plane curves to round points Journal of Differential Geometry. ,vol. 26, pp. 285- 314 ,(1987) , 10.4310/JDG/1214441371
Benjamin B. Kimia, Allen Tannenbaum, Steven W. Zucker, Toward a computational theory of shape: an overview european conference on computer vision. pp. 402- 407 ,(1990) , 10.1007/BFB0014889
M. Gage, R. S. Hamilton, The heat equation shrinking convex plane curves Journal of Differential Geometry. ,vol. 23, pp. 69- 96 ,(1986) , 10.4310/JDG/1214439902
Peter D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves ,(1987)
G.I. Sivashinsky, Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations Acta Astronautica. ,vol. 4, pp. 1177- 1206 ,(1977) , 10.1016/0094-5765(77)90096-0
E. Ben-Jacob, Nigel Goldenfeld, J. S. Langer, Gerd Schön, Dynamics of Interfacial Pattern Formation Physical Review Letters. ,vol. 51, pp. 1930- 1932 ,(1983) , 10.1103/PHYSREVLETT.51.1930
Stanley Osher, James A Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations Journal of Computational Physics. ,vol. 79, pp. 12- 49 ,(1988) , 10.1016/0021-9991(88)90002-2
P. D. Lax, Hyperbolic systems of conservation laws II Communications on Pure and Applied Mathematics. ,vol. 10, pp. 537- 566 ,(1957) , 10.1002/CPA.3160100406
Richard C. Brower, David A. Kessler, Joel Koplik, Herbert Levine, Geometrical models of interface evolution Physical Review A. ,vol. 29, pp. 1335- 1342 ,(1984) , 10.1103/PHYSREVA.29.1335