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

Anas Tiarimti Alaoui | Zendy; Mostafa Jourhmane | Zendy

Open Access

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

Author(s) -

Anas Tiarimti Alaoui,

Mostafa Jourhmane

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/5553126

Subject(s) - mathematics , uniqueness , monotonic function , anisotropic diffusion , a priori and a posteriori , nonlinear system , partial differential equation , mathematical analysis , weak solution , boundary value problem , image (mathematics) , computer science , philosophy , physics , epistemology , quantum mechanics , artificial intelligence

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.

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