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Volumn 37, Issue 5, 2006, Pages 1657-1687

Global solutions to the gradient flow equation of a nonconvex functional

Author keywords

Finite element method; Forward backward parabolic equations; Nonconvex functionals

Indexed keywords

FINITE ELEMENT METHOD; FUNCTION EVALUATION; PROBLEM SOLVING;

EID: 33748847571     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/050625333     Document Type: Article
Times cited : (19)

References (36)
  • 1
    • 0012520952 scopus 로고    scopus 로고
    • A new approach to variational problems with multiple scales
    • G. ALBERTI AND S. MÜLLER, A new approach to variational problems with multiple scales, Comm. Pure Appl. Math., 54 (2001), pp. 761-825.
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 761-825
    • Alberti, G.1    Müller, S.2
  • 2
    • 33748882071 scopus 로고    scopus 로고
    • Gradient flows in metric spaces and in the space of probability measures
    • ETH Zurich, Birkhäuser Verlag, Basel
    • L. AMBROSIO, N. GIQLI, AND G. SAVARÉ, Gradient Flows in Metric Spaces and in the Space of Probability Measures, Lectures Math. ETH Zurich, Birkhäuser Verlag, Basel, 2005.
    • (2005) Lectures Math.
    • Ambrosio, L.1    Giqli, N.2    Savaré, G.3
  • 5
    • 0040682601 scopus 로고
    • A degenerate pseudoparabolic regularisation of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow
    • G. I. B ARENBLATT, M. BERTSCH, R. DAL PASSO, AND M. UGHI, A degenerate pseudoparabolic regularisation of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow, SIAM J. Math. Anal., 24 (1993), pp. 1414-1439.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 1414-1439
    • Arenblatt, G.I.B.1    Bertsch, M.2    Dal Passo, R.3    Ughi, M.4
  • 6
    • 0027397245 scopus 로고
    • A mathematical model of turbulent heat and mass transfer in stably stratified shear flow
    • G. I. BARENBLATT, M. BERTSCH, R. DAL PASSO, V. M. PROSTOKISHIN, AND M. UGHI, A mathematical model of turbulent heat and mass transfer in stably stratified shear flow, J. Fluid Mech., 253 (1993), pp. 341-358.
    • (1993) J. Fluid Mech. , vol.253 , pp. 341-358
    • Barenblatt, G.I.1    Bertsch, M.2    Dal Passo, R.3    Prostokishin, V.M.4    Ughi, M.5
  • 9
    • 33748869769 scopus 로고    scopus 로고
    • Preprint Centro De Giorgi, Scuola Normale Superiore di Pisa, Pisa, Italy, submitted
    • x, Preprint Centro De Giorgi, Scuola Normale Superiore di Pisa, Pisa, Italy, 2005, submitted.
    • (2005) x
    • Bellettini, G.1    Fusco, G.2    Guglielmi, N.3
  • 10
    • 0009143376 scopus 로고    scopus 로고
    • Minimal barriers for geometric evolutions
    • G. BELLETTINI AND M. NOVAGA, Minimal barriers for geometric evolutions, J. Differential Equations, 139 (1997), pp. 76-103.
    • (1997) J. Differential Equations , vol.139 , pp. 76-103
    • Bellettini, G.1    Novaga, M.2
  • 13
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • F. CATTÉ, P.-L. LIONS, J.-M. MOREL, AND T. COLL, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29 (1992), pp. 182-193.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 182-193
    • Catté, F.1    Lions, P.-L.2    Morel, J.-M.3    Coll, T.4
  • 14
    • 0029328073 scopus 로고
    • Image segmentation by variational methods: Mumford-Shah functional and the discrete approximations
    • A. CHAMBOLLE, Image segmentation by variational methods: Mumford-Shah functional and the discrete approximations, SIAM J. Appl. Math., 55 (1995), pp. 827-863.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 827-863
    • Chambolle, A.1
  • 15
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. GRAND ALL, H. ISHII, AND P. L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull Amer. Math. Soc. (N.S.), 27 (1992), pp. 1-67.
    • (1992) Bull Amer. Math. Soc. (N.S.) , vol.27 , pp. 1-67
    • Grand All, M.G.1    Ishii, H.2    Lions, P.L.3
  • 17
    • 33748868231 scopus 로고    scopus 로고
    • Su olcuni problemi instabili legati alia teoria della visions
    • T. Bruno, P. Buonocore, L. Carbone, and V. Esposito, eds., La Città del Sole, Napoli, Italy
    • E. DE GIORGI, Su olcuni problemi instabili legati alia teoria della visions, in Atti del Convegno in onore di Carlo Ciliberto (Napoli, 1995), T. Bruno, P. Buonocore, L. Carbone, and V. Esposito, eds., La Città del Sole, Napoli, Italy, 1997, pp. 91-98.
    • (1997) Atti Del Convegno in Onore di Carlo Ciliberto (Napoli, 1995) , pp. 91-98
    • De Giorgi, E.1
  • 18
    • 0003164476 scopus 로고
    • Congetture riguardanti alcuni problemi di evoluzione
    • E. DE GlORGI, Congetture riguardanti alcuni problemi di evoluzione, Duke Math. J., 81 (1995), pp. 255-268.
    • (1995) Duke Math. J. , vol.81 , pp. 255-268
    • De Glorgi, E.1
  • 19
    • 0030526460 scopus 로고    scopus 로고
    • Young measure solutions for a nonlinear parabolic equation of forward-backward type
    • S. DEMOULINI, Young measure solutions for a nonlinear parabolic equation of forward-backward type, SIAM J. Math. Anal., 27 (1996), pp. 376-403.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 376-403
    • Demoulini, S.1
  • 20
    • 0035619136 scopus 로고    scopus 로고
    • An analysis of the Perona-Malik scheme
    • S. ESEDOGLU, An analysis of the Perona-Malik scheme, Comm. Pure Appl. Math., 54 (2001), pp. 1442-1487.
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 1442-1487
    • Esedoglu, S.1
  • 21
    • 0032329021 scopus 로고    scopus 로고
    • Numerical simulations of mean curvature flow in presence of a nonconvex anisotropy
    • F. FIERRO, R. GOOLIONE, AND M. PAOLINI, Numerical simulations of mean curvature flow in presence of a nonconvex anisotropy, Math. Models Methods Appl. Sci., 8 (1998), pp. 573-301.
    • (1998) Math. Models Methods Appl. Sci. , vol.8 , pp. 573-1301
    • Fierro, F.1    Goolione, R.2    Paolini, M.3
  • 22
    • 0037494077 scopus 로고    scopus 로고
    • Gradient flow for the one-dimensional Mumford-Shah functional
    • M. GOBBINO, Gradient flow for the one-dimensional Mumford-Shah functional, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 27 (1998), pp. 145-193.
    • (1998) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.27 , pp. 145-193
    • Gobbino, M.1
  • 24
    • 0040219530 scopus 로고
    • Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles
    • M. E. GURTIN, H.-M. SONER, AND P. E. SOUGANIDIS, Anisotropic motion of an interface relaxed by the formation of infinitesimal wrinkles, J. Differential Equations, 119 (1995), pp. 54-108.
    • (1995) J. Differential Equations , vol.119 , pp. 54-108
    • Gurtin, M.E.1    Soner, H.-M.2    Souganidis, P.E.3
  • 26
    • 84967713009 scopus 로고
    • Existence of infinitely many solutions for a forward-backward heat equation
    • K. HÖLLIG, Existence of infinitely many solutions for a forward-backward heat equation, Trans. Amer. Math. Soc., 278 (1983), pp. 299-316.
    • (1983) Trans. Amer. Math. Soc. , vol.278 , pp. 299-316
    • Höllig, K.1
  • 27
    • 0006940464 scopus 로고
    • A diffusion equation with a nonmonotone constitutive function
    • J. Ball, ed., D. Reidel, Boston, MA
    • K. HÖLLIG AND J. A. NOHEL, A diffusion equation with a nonmonotone constitutive function, in Systems of Nonlinear Differential Equations, J. Ball, ed., D. Reidel, Boston, MA, 1983,pp. 409-422.
    • (1983) Systems of Nonlinear Differential Equations , pp. 409-422
    • Höllig, K.1    Nohel, J.A.2
  • 28
    • 0032382150 scopus 로고    scopus 로고
    • Maximum and comparison principle for one-dimensional anisotropic diffusion
    • B. KAWOHL AND N. KUTEV, Maximum and comparison principle for one-dimensional anisotropic diffusion, Math. Ann., 311 (1998), pp. 107-123.
    • (1998) Math. Ann. , vol.311 , pp. 107-123
    • Kawohl, B.1    Kutev, N.2
  • 29
    • 0031256990 scopus 로고    scopus 로고
    • The Perona-Malik paradox
    • S. KlCHENASSAMY, The Perona-Malik paradox, SIAM J. Appl. Math., 57 (1997), pp. 1328-1342.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1328-1342
    • Klchenassamy, S.1
  • 32
    • 0041049212 scopus 로고    scopus 로고
    • ∞ bound for a time-discrete regularization of a forward-backward parabolic equation
    • ∞ bound for a time-discrete regularization of a forward-backward parabolic equation, Indiana Univ. Math. J., 45 (1996), pp. 683-693.
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 683-693
    • Muler, N.E.1
  • 34
    • 0025465145 scopus 로고
    • Scale space and edge detection using anisotropic diffusion
    • P. PERONA AND J. MALIK, Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., 12 (1990), pp. 629-639.
    • (1990) IEEE Trans. Pattern Anal. Mach. Intell. , vol.12 , pp. 629-639
    • Perona, P.1    Malik, J.2
  • 35
    • 0012945863 scopus 로고
    • Passage to the limit with respect to viscosity in an equation with variable parabolicity direction
    • P. I. PLOTNIKOV, Passage to the limit with respect to viscosity in an equation with variable parabolicity direction, Differential Equations, 30 (1994), pp. 614-622.
    • (1994) Differential Equations , vol.30 , pp. 614-622
    • Plotnikov, P.I.1
  • 36
    • 33748848417 scopus 로고
    • Dynamics of measured valued solutions to a backward-forward heat equation
    • M. SLEMROD, Dynamics of measured valued solutions to a backward-forward heat equation, 3. Dynam. Differential Equations, 3 (1991), pp. 614-622.
    • (1991) 3. Dynam. Differential Equations , vol.3 , pp. 614-622
    • Slemrod, M.1


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