Entire Solutions of the One-Dimensional Perona-Malik Equation

DOI10.1080/03605300600634981zbMath1134.35062OpenAlexW2253847539MaRDI QIDQ5294661

Massimo Gobbino

Publication date: 25 July 2007

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300600634981

zbMATH Keywords

entire solutionanisotropic diffusionPerona-Malik equationfinite time blow upforward-backward parabolic equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (16)

Classification of equilibria and \(\Gamma \)-convergence for the discrete Perona-Malik functional ⋮ PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW ⋮ Gradient estimates for the Perona-Malik equation ⋮ Rate of convergence for one-dimensional quasilinear parabolic problem and its applications ⋮ The $\Gamma $-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type ⋮ 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 ⋮ The Γ-limit for singularly perturbed functionals of Perona–Malik type in arbitrary dimension ⋮ Radial weak solutions for the Perona-Malik equation as a differential inclusion ⋮ Wavefront solutions to reaction-convection equations with Perona-Malik diffusion ⋮ A new nonlocal nonlinear diffusion of image processing ⋮ An Example of Global Classical Solution for the Perona-Malik Equation ⋮ A class of local classical solutions for the one-dimensional Perona-Malik equation ⋮ Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions

Cites Work

• A concept of solution and numerical experiments for forward-backward diffusion equations
• Gradient estimates for the Perona-Malik equation
• Axioms and fundamental equations of image processing
• Maximum and comparison principle for one-dimensional anisotropic diffusion
• Existence of Infinitely Many Solutions for a Forward Backward Heat Equation
• From Mumford–Shah to Perona–Malik in image processing
• Stability Properties of the Perona--Malik Scheme
• The Perona--Malik Paradox
• An analysis of the Perona-Malik scheme
• Global Solutions to the Gradient Flow Equation of a Nonconvex Functional

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