TY - JOUR A2 - Cho, Sun Young AU - Tiarimti Alaoui, Anas AU - Jourhmane, Mostafa PY - 2021 DA - 2021/03/08 TI - Existence and Uniqueness of Weak Solutions for Novel Anisotropic Nonlinear Diffusion Equations Related to Image Analysis SP - 5553126 VL - 2021 AB - 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. SN - 2314-4629 UR - https://doi.org/10.1155/2021/5553126 DO - 10.1155/2021/5553126 JF - Journal of Mathematics PB - Hindawi KW - ER -