Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis
This paper establishes the existence and uniqueness of weak solutions for the initial-boundary value problem of anisotropic nonlinear diffusion partial differential equations related to image processing and analysis. An implicit iterative method combined with a variational approach has been applied...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5553126 |
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| _version_ | 1850210043019919360 |
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| author | Anas Tiarimti Alaoui Mostafa Jourhmane |
| author_facet | Anas Tiarimti Alaoui Mostafa Jourhmane |
| author_sort | Anas Tiarimti Alaoui |
| collection | DOAJ |
| description | This paper establishes the existence and uniqueness of weak solutions for the initial-boundary value problem of anisotropic nonlinear diffusion partial differential equations related to image processing and analysis. An implicit iterative method combined with a variational approach has been applied to construct approximate solutions for this problem. Then, under some a priori estimates and a monotonicity condition, the existence of unique weak solutions for this problem has been proven. This work has been complemented by a consistent and stable approximation scheme showing its great significance as an image restoration technique. |
| format | Article |
| id | doaj-art-976dbab4e29541519cbdc6b38c5dd5eb |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-976dbab4e29541519cbdc6b38c5dd5eb2025-08-20T02:09:51ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55531265553126Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image AnalysisAnas Tiarimti Alaoui0Mostafa Jourhmane1TIAD Laboratory, Department of Mathematics, Faculty of Sciences and Technology, Sultan Moulay Slimane University, Beni Mellal 23000, MoroccoTIAD Laboratory, Department of Mathematics, Faculty of Sciences and Technology, Sultan Moulay Slimane University, Beni Mellal 23000, MoroccoThis paper establishes the existence and uniqueness of weak solutions for the initial-boundary value problem of anisotropic nonlinear diffusion partial differential equations related to image processing and analysis. An implicit iterative method combined with a variational approach has been applied to construct approximate solutions for this problem. Then, under some a priori estimates and a monotonicity condition, the existence of unique weak solutions for this problem has been proven. This work has been complemented by a consistent and stable approximation scheme showing its great significance as an image restoration technique.http://dx.doi.org/10.1155/2021/5553126 |
| spellingShingle | Anas Tiarimti Alaoui Mostafa Jourhmane Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis Journal of Mathematics |
| title | Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis |
| title_full | Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis |
| title_fullStr | Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis |
| title_full_unstemmed | Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis |
| title_short | Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis |
| title_sort | existence and uniqueness of weak solutions for novel anisotropic nonlinear diffusion equations related to image analysis |
| url | http://dx.doi.org/10.1155/2021/5553126 |
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