A class of thin-film equations with space-time dependent gradient nonlinearity and its application to image sharpening
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909595701608448 |
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| author | Li, Yuhang Guo, Zhichang Song, Fanghui Wu, Boying Guo, Bin |
| author_facet | Li, Yuhang Guo, Zhichang Song, Fanghui Wu, Boying Guo, Bin |
| contents | We introduce a class of thin-film equations with space-time dependent gradient nonlinearity and apply them to image sharpening. By modifying the potential well method, we overcome the challenges arising from variable exponents and the "moving" Nehari manifold, thereby providing a classification of global existence and finite time blow-up of solutions under different initial conditions. Decay rates for global solutions and lifespan estimates for blow-up solutions are also established. Numerical experiments demonstrate the effectiveness of this class of equations as image sharpening models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A class of thin-film equations with space-time dependent gradient nonlinearity and its application to image sharpening Li, Yuhang Guo, Zhichang Song, Fanghui Wu, Boying Guo, Bin Analysis of PDEs We introduce a class of thin-film equations with space-time dependent gradient nonlinearity and apply them to image sharpening. By modifying the potential well method, we overcome the challenges arising from variable exponents and the "moving" Nehari manifold, thereby providing a classification of global existence and finite time blow-up of solutions under different initial conditions. Decay rates for global solutions and lifespan estimates for blow-up solutions are also established. Numerical experiments demonstrate the effectiveness of this class of equations as image sharpening models. |
| title | A class of thin-film equations with space-time dependent gradient nonlinearity and its application to image sharpening |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.19211 |