An Example of Global Classical Solution for the Perona-Malik Equation
Article Properties
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LanguageEnglish
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DOI (url)
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Publication Date2011/08/01
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Indian UGC (journal)
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Refrences19
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Citations8
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Marina Ghisi
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Massimo Gobbino
Cite
Ghisi, Marina, and Massimo Gobbino. “An Example of Global Classical Solution for the Perona-Malik Equation”. Communications in Partial Differential Equations, vol. 36, no. 8, 2011, pp. 1318-52, https://doi.org/10.1080/03605302.2010.542672.
Ghisi, M., & Gobbino, M. (2011). An Example of Global Classical Solution for the Perona-Malik Equation. Communications in Partial Differential Equations, 36(8), 1318-1352. https://doi.org/10.1080/03605302.2010.542672
Ghisi, Marina, and Massimo Gobbino. “An Example of Global Classical Solution for the Perona-Malik Equation”. Communications in Partial Differential Equations 36, no. 8 (2011): 1318-52. https://doi.org/10.1080/03605302.2010.542672.
Ghisi M, Gobbino M. An Example of Global Classical Solution for the Perona-Malik Equation. Communications in Partial Differential Equations. 2011;36(8):1318-52.
Journal Categories
Science
Mathematics
Technology
Technology (General)
Industrial engineering
Management engineering
Applied mathematics
Quantitative methods
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Refrences
| Title | Journal | Journal Categories | Citations | Publication Date |
|---|---|---|---|---|
Upper bounds on the coarsening rate of discrete, ill‐posed nonlinear diffusion equations | Communications on Pure and Applied Mathematics |
| 9 | 2009 |
| Upper bounds on the coarsening rate of discrete, ill‐posed nonlinear diffusion equations | 2007 | |||
| Linear And Quasilinear Equations of Parabolic Type | 1967 | |||
| Existence of infinitely many solutions for the one-dimensional Perona-Malik model | Calculus of Variations and Partial Differential Equations |
| 36 | 2006 |
| Young measure solutions and instability of the one-dimensional Perona–Malik equation | Journal of Mathematical Analysis and Applications |
| 14 | 2005 |
Citations
| Title | Journal | Journal Categories | Citations | Publication Date |
|---|---|---|---|---|
| On Lipschitz solutions for some forward–backward parabolic equations | Annales de l'Institut Henri Poincaré C, Analyse non linéaire |
| 12 | 2018 |
| On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems | Nonlinearity |
| 1 | 2018 |
| Radial weak solutions for the Perona–Malik equation as a differential inclusion | Journal of Differential Equations |
| 7 | 2015 |
| Convex Integration and Infinitely Many Weak Solutions to the Perona--Malik Equation in All Dimensions | SIAM Journal on Mathematical Analysis |
| 2015 | |
| A backward–forward regularization of the Perona–Malik equation | Journal of Differential Equations |
| 20 | 2012 |
Citations Analysis
| Category | Category Repetition |
|---|---|
| Science: Mathematics | 7 |
| Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods | 5 |
The category
Science: Mathematics 7
is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled Slow Time Behavior of the Semidiscrete Perona–Malik Scheme in One Dimension and was published in 2011. The most recent citation comes from a 2018 study titled On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems. This article reached its peak citation in 2012, with 3 citations. It has been cited in 6 different journals, 16% of which are open access. Among related journals, the SIAM Journal on Mathematical Analysis cited this research the most, with 2 citations. The chart below illustrates the annual citation trends for this article.