Young measure solutions and instability of the one-dimensional Perona–Malik equation
Article Properties
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LanguageEnglish
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DOI (url)
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Publication Date2005/08/01
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Indian UGC (journal)
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Refrences44
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Citations14
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Shahnaz Taheri
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Qi Tang
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Kewei Zhang
Cite
Taheri, Shahnaz, et al. “Young Measure Solutions and Instability of the One-Dimensional Perona–Malik Equation”. Journal of Mathematical Analysis and Applications, vol. 308, no. 2, 2005, pp. 467-90, https://doi.org/10.1016/j.jmaa.2004.11.034.
Taheri, S., Tang, Q., & Zhang, K. (2005). Young measure solutions and instability of the one-dimensional Perona–Malik equation. Journal of Mathematical Analysis and Applications, 308(2), 467-490. https://doi.org/10.1016/j.jmaa.2004.11.034
Taheri S, Tang Q, Zhang K. Young measure solutions and instability of the one-dimensional Perona–Malik equation. Journal of Mathematical Analysis and Applications. 2005;308(2):467-90.
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 |
|---|---|---|---|---|
| The Regularity of Critical Points of Polyconvex Functionals | Archive for Rational Mechanics and Analysis |
| 35 | 2004 |
| Young measure solutions for a class of forward–backward diffusion equations | Journal of Mathematical Analysis and Applications |
| 2003 | |
| Convex integration for Lipschitz mappings and counterexamples to regularity | Annals of Mathematics |
| 126 | 2003 |
| Maximum and comparison principle for one-dimensional anisotropic diffusion | Mathematische Annalen |
| 46 | 1998 |
| On various semiconvex hulls in the calculus of variations | Calculus of Variations and Partial Differential Equations |
| 13 | 1998 |
Citations
| Title | Journal | Journal Categories | Citations | Publication Date |
|---|---|---|---|---|
| Hierarchical Controllability for a Nonlinear Parabolic Equation in One Dimension | Journal of Optimization Theory and Applications |
| 2023 | |
| On Lipschitz solutions for some forward–backward parabolic equations | Annales de l'Institut Henri Poincaré C, Analyse non linéaire |
| 12 | 2018 |
| Approximations for modulus of gradients and their applications to neighborhood filters | Frontiers of Mathematics in China |
| 8 | 2013 |
| A backward–forward regularization of the Perona–Malik equation | Journal of Differential Equations |
| 20 | 2012 |
PASSING TO THE LIMIT IN MAXIMAL SLOPE CURVES: FROM A REGULARIZED PERONA–MALIK EQUATION TO THE TOTAL VARIATION FLOW | Mathematical Models and Methods in Applied Sciences |
| 2012 |
Citations Analysis
The category
Science: Mathematics 12
is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled Existence of infinitely many solutions for the one-dimensional Perona-Malik model and was published in 2006. The most recent citation comes from a 2023 study titled Hierarchical Controllability for a Nonlinear Parabolic Equation in One Dimension. This article reached its peak citation in 2012, with 3 citations. It has been cited in 12 different journals, 8% of which are open access. Among related journals, the Mathematical Models and Methods in Applied Sciences cited this research the most, with 2 citations. The chart below illustrates the annual citation trends for this article.