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Volumn 35, Issue 3, 2001, Pages 437-462

On the approximation of front propagation problems with nonlocal terms

Author keywords

Front propagation; Thinning

Indexed keywords


EID: 0035593510     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2001120     Document Type: Article
Times cited : (7)

References (27)
  • 2
    • 0040305878 scopus 로고    scopus 로고
    • Geometric evolution problems, distance function and viscosity solutions
    • G. Buttazzo et al. Eds., Based on a summer school, Pisa, Italy, September 1996, Springer, Berlin
    • L. Ambrosio, 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 .
    • (2000) Calculus of Variations and Partial Differential Equations. Topics on Geometrical Evolution Problems and Degree Theory , pp. 5-93
    • Ambrosio, L.1
  • 3
    • 0001055754 scopus 로고
    • A simple proof of convergence for an approximation scheme for computing motions by mean curvature
    • G. Barles and C. Georgelin, A simple proof of convergence for an approximation scheme for computing motions by mean curvature. SIAM J. Numer. Anal. 32 (1995) 484-500.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 484-500
    • Barles, G.1    Georgelin, C.2
  • 4
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • G. Barles and P.M. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis 4 (1991) 271-283.
    • (1991) Asymptotic Analysis , vol.4 , pp. 271-283
    • Barles, G.1    Souganidis, P.M.2
  • 6
    • 0032386084 scopus 로고    scopus 로고
    • A new approach to front propagation problems: Theory and applications
    • G. Barles and P.M. Souganidis, A new approach to front propagation problems: theory and applications. Arch. Ration. Mech. Anal. 141 (1998) 237-296.
    • (1998) Arch. Ration. Mech. Anal. , vol.141 , pp. 237-296
    • Barles, G.1    Souganidis, P.M.2
  • 7
    • 0015581337 scopus 로고
    • Biological shape and visual science
    • H. Blum, Biological shape and visual science. J. Theor. Biology 38 (1973) 205-287.
    • (1973) J. Theor. Biology , vol.38 , pp. 205-287
    • Blum, H.1
  • 9
    • 0000474114 scopus 로고    scopus 로고
    • On front propagation problems with nonlocal terms
    • P. Cardaliaguet, On front propagation problems with nonlocal terms. Adv. Differential Equation 5 (1999) 213-268.
    • (1999) Adv. Differential Equation , vol.5 , pp. 213-268
    • Cardaliaguet, P.1
  • 10
    • 0032210517 scopus 로고    scopus 로고
    • Partial differential equations and mathematical morphology
    • F. Cao, Partial differential equations and mathematical morphology. J. Math. Pures Appl. 77 (1998) 909-941.
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 909-941
    • Cao, F.1
  • 11
    • 84965008631 scopus 로고
    • A morphological scheme for mean curvature motion
    • F. Catte, F. Dibos and G. Koepfler, A morphological scheme for mean curvature motion. SIAM J. Numer. Anal. 32 (1995) 1895-1909.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1895-1909
    • Catte, F.1    Dibos, F.2    Koepfler, G.3
  • 12
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Y. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differential Geom. 33 (1991) 749-786.
    • (1991) J. Differential Geom. , vol.33 , pp. 749-786
    • Chen, Y.1    Giga, Y.2    Goto, S.3
  • 13
    • 0031126459 scopus 로고    scopus 로고
    • Asymptotic behavior of solutions of an Allen-Cahn equation with a nonlocal term
    • X. Chen, D. Hilhorst and E. Logak, Asymptotic behavior of solutions of an Allen-Cahn equation with a nonlocal term. Nonlinear Anal. T.M.A. 28 (1997) 1283-1298.
    • (1997) Nonlinear Anal. T.M.A. , vol.28 , pp. 1283-1298
    • Chen, X.1    Hilhorst, D.2    Logak, E.3
  • 14
    • 84967708673 scopus 로고
    • User's guide to viscosity solution of second order partial differential equations
    • M. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solution of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67.
    • (1992) Bull. Amer. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.-L.3
  • 15
    • 0030507383 scopus 로고    scopus 로고
    • Convergent difference schemes for nonlinear parabolic equations and mean curvature motion
    • M. Crandall and P.-L. Lions, Convergent difference schemes for nonlinear parabolic equations and mean curvature motion. Numer. Math. 75 (1996) 17-41.
    • (1996) Numer. Math. , vol.75 , pp. 17-41
    • Crandall, M.1    Lions, P.-L.2
  • 17
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature I
    • L.C. Evans and J. Spruck, Motion of level sets by mean curvature I. J. Differential Geom. 33 (1991) 635-681.
    • (1991) J. Differential Geom. , vol.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 18
    • 0000357774 scopus 로고
    • Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains
    • Y. Giga, S. Goto, H. Ishii and M.-H. Sato, Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains. Indiana Univ. Math. J. 40 (1990) 443-470.
    • (1990) Indiana Univ. Math. J. , vol.40 , pp. 443-470
    • Giga, Y.1    Goto, S.2    Ishii, H.3    Sato, M.-H.4
  • 20
    • 0001081134 scopus 로고
    • A generalization of the Bence-Merriman and Osher algorithm for motion by mean curvature
    • Proceedings of the international conference on curvature flows and related topics, Levico, Italy, June 27 - July 2nd 1994, A. Damlamian et al. Eds. Gakkotosho, Tokyo
    • H. Ishii, 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 .
    • (1995) GAKUTO Int. Ser., Math. Sci. Appl. , vol.5 , pp. 111-127
    • Ishii, H.1
  • 21
    • 0039121838 scopus 로고    scopus 로고
    • Gauss curvature flow and its approximation
    • Proceedings of the international conference on free boundary problems: theory and applications, Chiba, Japan, November 7-13 1999, N. Kenmochi Ed. Gakkotosho, Tokyo
    • H. Ishii, 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.
    • (2000) GAKUTO Int. Ser., Math. Sci. Appl. , vol.14 , pp. 198-206
    • Ishii, H.1
  • 22
    • 44749084234 scopus 로고    scopus 로고
    • Front propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. Osher and J.A. Sethian, Front propagation with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comp. Phys. 79 (1998) 12-49.
    • (1998) J. Comp. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 24
    • 0033276568 scopus 로고    scopus 로고
    • Approximation of viscosity solution by morphological filters
    • D. Pasquignon, Approximation of viscosity solution by morphological filters. ESAIM: COCV 4 (1999) 335-359.
    • (1999) ESAIM: COCV , vol.4 , pp. 335-359
    • Pasquignon, D.1
  • 25
    • 0006100640 scopus 로고    scopus 로고
    • Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science
    • Cambridge University Press, Cambridge
    • J.A. Sethian, 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).
    • (1996) Cambridge Monographs Appl. Comput. Math. , vol.3
    • Sethian, J.A.1
  • 26
    • 0039232937 scopus 로고
    • Front propagation
    • Boundaries, interfaces and transitions, Banff, AB, Amer. Math. Soc., Providence RI
    • H.M. Soner, Front propagation, in Boundaries, interfaces and transitions, (Banff, AB, 1995) CRM Proc. Lect. Notes 13, Amer. Math. Soc., Providence RI (1998) 185-206.
    • (1995) CRM Proc. Lect. Notes , vol.13 , pp. 185-206
    • Soner, H.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.