A class of local classical solutions for the one-dimensional Perona-Malik equation

DOI10.1090/S0002-9947-09-04793-XzbMath1213.35320OpenAlexW2083467223MaRDI QIDQ3648200

Marina Ghisi, Massimo Gobbino

Publication date: 24 November 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-09-04793-x

zbMATH Keywords

one space dimensionanisotropic diffusionsupersolutionshomogeneous Neumann boundary conditionsforward-backward parabolic equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate parabolic equations (35K65) Initial-boundary value problems for PDEs of mixed type (35M13) Comparison principles in context of PDEs (35B51)

Related Items (13)

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 ⋮ On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems ⋮ On Lipschitz solutions for some forward-backward parabolic equations ⋮ Hierarchical controllability for a nonlinear parabolic equation in one dimension ⋮ Qualitative properties for Perona-Malik type equations ⋮ Upper bounds on the coarsening rate of discrete, ill‐posed nonlinear diffusion equations ⋮ A backward-forward regularization of the Perona-Malik equation ⋮ CONVERGENCE FOR LONG-TIMES OF A SEMIDISCRETE PERONA–MALIK EQUATION IN ONE DIMENSION ⋮ Radial weak solutions for the Perona-Malik equation as a differential inclusion ⋮ A new nonlocal nonlinear diffusion of image processing ⋮ An Example of Global Classical Solution for the Perona-Malik Equation ⋮ Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions

Cites Work

• Optimal regularity for one-dimensional porous medium flow
• Gradient estimates for the Perona-Malik equation
• Maximum and comparison principle for one-dimensional anisotropic diffusion
• Young measure solutions of the two-dimensional Perona-Malik equation in image processing
• Young measure solutions and instability of the one-dimensional Perona-Malik equation
• Existence of infinitely many solutions for the one-dimensional Perona-Malik model
• Existence of Infinitely Many Solutions for a Forward Backward Heat Equation
• Stability Properties of the Perona--Malik Scheme
• The $\Gamma $-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type
• The Perona--Malik Paradox
• An analysis of the Perona-Malik scheme
• Entire Solutions of the One-Dimensional Perona-Malik Equation
• Global Solutions to the Gradient Flow Equation of a Nonconvex Functional
• Regularity Propeties of Flows Through Porous Media

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