A class of forward-backward regularizations of the Perona-Malik equation with variable exponent
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918290911133696 |
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| author | Tong, Yihui Liu, Wenjie Guo, Zhichang Yao, Wenjuan |
| author_facet | Tong, Yihui Liu, Wenjie Guo, Zhichang Yao, Wenjuan |
| contents | This paper investigates a novel class of regularizations of the Perona-Malik equation with variable exponents, of forward-backward parabolic type, which possess a variational structure and have potential applications in image processing. The existence of Young measure solutions to the Neumann initial-boundary value problem for the proposed equation is established via Sobolev approximation and the vanishing viscosity limit. The proofs rely on Rothe's method, variational principles, and Young measure theory. The theoretical results confirm numerical observations concerning the generic behavior of solutions with suitably chosen variable exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A class of forward-backward regularizations of the Perona-Malik equation with variable exponent Tong, Yihui Liu, Wenjie Guo, Zhichang Yao, Wenjuan Analysis of PDEs This paper investigates a novel class of regularizations of the Perona-Malik equation with variable exponents, of forward-backward parabolic type, which possess a variational structure and have potential applications in image processing. The existence of Young measure solutions to the Neumann initial-boundary value problem for the proposed equation is established via Sobolev approximation and the vanishing viscosity limit. The proofs rely on Rothe's method, variational principles, and Young measure theory. The theoretical results confirm numerical observations concerning the generic behavior of solutions with suitably chosen variable exponents. |
| title | A class of forward-backward regularizations of the Perona-Malik equation with variable exponent |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.23982 |