CONVERGENCE FOR LONG-TIMES OF A SEMIDISCRETE PERONA–MALIK EQUATION IN ONE DIMENSION

DOI10.1142/S0218202511005040zbMath1218.35034OpenAlexW2074742224MaRDI QIDQ3007771

Matteo Novaga, Giovanni Bellettini, Maurizio Paolini

Publication date: 17 June 2011

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202511005040

zbMATH Keywords

nonconvex functionalssemidiscrete schemeforward-backward parabolic equationsdiscrete comparison functions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Maximum principles in context of PDEs (35B50) A priori estimates in context of PDEs (35B45) Comparison principles in context of PDEs (35B51)

Related Items (6)

Diffusion, pre-smoothing and gradient descent ⋮ PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW ⋮ Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations ⋮ Measure-Valued Solutions to a Nonlinear Fourth-Order Regularization of Forward-Backward Parabolic Equations ⋮ A backward-forward regularization of the Perona-Malik equation ⋮ A new nonlocal nonlinear diffusion of image processing

Cites Work

• Classification of equilibria and \(\Gamma \)-convergence for the discrete Perona-Malik functional
• Convergence of discrete schemes for the Perona-Malik equation
• Dynamics of measured valued solutions to a backward-forward heat equation
• Maximum and comparison principle for one-dimensional anisotropic diffusion
• Relations between regularization and diffusion filtering
• Young measure solutions and instability of the one-dimensional Perona-Malik equation
• The $\Gamma $-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type
• A class of local classical solutions for the one-dimensional Perona-Malik equation
• Image Selective Smoothing and Edge Detection by Nonlinear Diffusion
• NUMERICAL SIMULATIONS OF MEAN CURVATURE FLOW IN THE PRESENCE OF A NONCONVEX ANISOTROPY
• The Perona--Malik Paradox
• Entire Solutions of the One-Dimensional Perona-Malik Equation
• Global Solutions to the Gradient Flow Equation of a Nonconvex Functional

This page was built for publication: CONVERGENCE FOR LONG-TIMES OF A SEMIDISCRETE PERONA–MALIK EQUATION IN ONE DIMENSION