Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis

Anas Tiarimti Alaoui, Mostafa Jourhmane and Sun Young Cho

Journal of Mathematics, 2021, vol. 2021, 1-18

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5553126

DOI: 10.1155/2021/5553126

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