A family of nonlinear diffusions connecting Perona-Malik to standard diffusion

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Guidotti, Patrick. “A Family of Nonlinear Diffusions Connecting Perona-Malik to Standard Diffusion”. Discrete &Amp; Continuous Dynamical Systems - S, vol. 5, no. 3, 2012, pp. 581-90, https://doi.org/10.3934/dcdss.2012.5.581.
Guidotti, P. (2012). A family of nonlinear diffusions connecting Perona-Malik to standard diffusion. Discrete &Amp; Continuous Dynamical Systems - S, 5(3), 581-590. https://doi.org/10.3934/dcdss.2012.5.581
Guidotti P. A family of nonlinear diffusions connecting Perona-Malik to standard diffusion. Discrete & Continuous Dynamical Systems - S. 2012;5(3):581-90.
Refrences
Title Journal Journal Categories Citations Publication Date
An Example of Global Classical Solution for the Perona-Malik Equation Communications in Partial Differential Equations
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 8 2011
A new well-posed nonlinear nonlocal diffusion Nonlinear Analysis
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 9 2010
A new nonlocal nonlinear diffusion of image processing Journal of Differential Equations
  • Science: Mathematics
 26 2009
Two New Nonlinear Nonlocal Diffusions for Noise Reduction Journal of Mathematical Imaging and Vision
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Technology: Mechanical engineering and machinery
  • Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
 45 2009
Existence of infinitely many solutions for the one-dimensional Perona-Malik model Calculus of Variations and Partial Differential Equations
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 36 2006
Refrences Analysis
Category Category Repetition
Science: Mathematics8
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods6
The category Science: Mathematics 8 is the most frequently represented among the references in this article. It primarily includes studies from SIAM Journal on Applied Mathematics and Mathematische Annalen. The chart below illustrates the number of referenced publications per year.
Refrences used by this article by year
Citations
Title Journal Journal Categories Citations Publication Date
A Non-Local Diffusion Equation for Noise Removal Acta Mathematica Scientia
  • Science: Mathematics
 2022
High-order anisotropic diffusion operators in spaces of variable exponents and application to image inpainting and restoration problems Nonlinear Analysis: Real World Applications
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 14 2019
A family of evolution equations connecting area-preserving to length-preserving curve flows Nonlinear Analysis: Real World Applications
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Science: Mathematics
 2 2018
A Class of Elliptic Equations with Interior Degeneration Journal of Mathematical Imaging and Vision
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software
  • Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
  • Technology: Mechanical engineering and machinery
  • Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics
  • Science: Mathematics: Instruments and machines: Electronic computers. Computer science
 2 2017
Citations Analysis
Category Category Repetition
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods3
Science: Mathematics3
Science: Mathematics: Instruments and machines: Electronic computers. Computer science1
Science: Mathematics: Instruments and machines: Electronic computers. Computer science: Computer software1
Technology: Mechanical engineering and machinery1
Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics1
The category Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods 3 is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled A Class of Elliptic Equations with Interior Degeneration and was published in 2017. The most recent citation comes from a 2022 study titled A Non-Local Diffusion Equation for Noise Removal. This article reached its peak citation in 2022, with 1 citations. It has been cited in 3 different journals. Among related journals, the Nonlinear Analysis: Real World Applications cited this research the most, with 2 citations. The chart below illustrates the annual citation trends for this article.
Citations used this article by year