We investigate the approximation of the evolution of compact hypersurfaces of depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.
Mots clés : front propagation, thinning
@article{M2AN_2001__35_3_437_0,
author = {Cardaliaguet, Pierre and Pasquignon, Denis},
title = {On the approximation of front propagation problems with nonlocal terms},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {437--462},
publisher = {EDP-Sciences},
volume = {35},
number = {3},
year = {2001},
mrnumber = {1837079},
zbl = {0992.65097},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_3_437_0/}
}
TY - JOUR AU - Cardaliaguet, Pierre AU - Pasquignon, Denis TI - On the approximation of front propagation problems with nonlocal terms JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 437 EP - 462 VL - 35 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_3_437_0/ LA - en ID - M2AN_2001__35_3_437_0 ER -
%0 Journal Article %A Cardaliaguet, Pierre %A Pasquignon, Denis %T On the approximation of front propagation problems with nonlocal terms %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 437-462 %V 35 %N 3 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_3_437_0/ %G en %F M2AN_2001__35_3_437_0
Cardaliaguet, Pierre; Pasquignon, Denis. On the approximation of front propagation problems with nonlocal terms. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 3, pp. 437-462. http://www.numdam.org/item/M2AN_2001__35_3_437_0/
[1] ,, and J-.M. Morel, Axioms and fundamental equations of image processing. Arch. Ration. Mech. Anal. 123 (1993) 199-257. | Zbl
[2] , Geometric evolution problems, distance function and viscosity solutions, in Calculus of variations and partial differential equations. Topics on geometrical evolution problems and degree theory, G. Buttazzo et al. Eds., Based on a summer school, Pisa, Italy, September 1996. Springer, Berlin (2000) 5-93; 327-337 . | Zbl
[3] and, A simple proof of convergence for an approximation scheme for computing motions by mean curvature. SIAM J. Numer. Anal. 32 (1995) 484-500. | Zbl
[4] and, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis 4 (1991) 271-283. | Zbl
[5] , and, Front propagation and phase field theory. SIAM J. Control Optim. 31 (1993) 439-469. | Zbl
[6] and, A new approach to front propagation problems: theory and applications. Arch. Ration. Mech. Anal. 141 (1998) 237-296. | Zbl
[7] , Biological shape and visual science. J. Theor. Biology 38 (1973) 205-287.
[8] , and, Diffusion motion generated by mean curvature. CAM Report 92-18. Dept of Mathematics. University of California Los Angeles (1992).
[9] , On front propagation problems with nonlocal terms. Adv. Differential Equation 5 (1999) 213-268. | Zbl
[10] , Partial differential equations and mathematical morphology. J. Math. Pures Appl. 77 (1998) 909-941. | Zbl
[11] , and, A morphological scheme for mean curvature motion. SIAM J. Numer. Anal. 32 (1995) 1895-1909. | Zbl
[12] , and, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differential Geom. 33 (1991) 749-786. | Zbl
[13] , and, Asymptotic behavior of solutions of an Allen-Cahn equation with a nonlocal term. Nonlinear Anal. T.M.A. 28 (1997) 1283-1298. | Zbl
[14] , and, User's guide to viscosity solution of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67. | Zbl
[15] and, Convergent difference schemes for nonlinear parabolic equations and mean curvature motion. Numer. Math. 75 (1996) 17-41. | Zbl
[16] and, Moving surfaces and abstract parabolic evolution equations. Topics in nonlinear analysis, Progr. Nonlinear Differential Equations Appl. 35, Birkhäuser, Basel (1999) 183-212. | Zbl
[17] and, Motion of level sets by mean curvature I. J. Differential Geom. 33 (1991) 635-681. | Zbl
[18] ,, and, Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains. Indiana Univ. Math. J. 40 (1990) 443-470. | Zbl
[19] and, Partial differential equation and image iterative filtering. Tutorial of ICIP 95, Washington D.C., (1995).
[20] , A generalization of the Bence-Merriman and Osher algorithm for motion by mean curvature, in Proceedings of the international conference on curvature flows and related topics, Levico, Italy, June 27 - July 2nd 1994, A. Damlamian et al. Eds. GAKUTO Int. Ser., Math. Sci. Appl. 5, Gakkotosho, Tokyo (1995) 111-127 . | Zbl
[21] , Gauss curvature flow and its approximation, in Proceedings of the international conference on free boundary problems: theory and applications, Chiba, Japan, November 7-13 1999, N. Kenmochi Ed. GAKUTO Int. Ser., Math. Sci. Appl. 14, Gakkotosho, Tokyo (2000) 198-206. | Zbl
[22] and, Front propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phys. 79 (1998) 12-49. | Zbl
[23] , Computation of skeleton by PDE. IEEE-ICIP, Washington (1995).
[24] , Approximation of viscosity solution by morphological filters. ESAIM: COCV 4 (1999) 335-359. | Numdam | Zbl
[25] , Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge Monographs Appl. Comput. Math. 3, Cambridge University Press, Cambridge (1996). | MR | Zbl
[26] , Front propagation, in Boundaries, interfaces and transitions, (Banff, AB, 1995) CRM Proc. Lect. Notes 13, Amer. Math. Soc., Providence RI (1998) 185-206. | Zbl
[27] , Files d'attentes et algorithmes morphologiques. Thèse mines de Paris (1992).
