A class of nonlinear parabolic systems having standard growth and L1 data. (October 2022)

• Record Type: Journal Article
• Authors: Atlas, Abdelghafour; Karami, Fahd; Meskine, Driss; Ouakrim, Youssef; Oubbih, Omar
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Image denoising -- Staircase effect -- Nonlinear inverse problems -- Nonlinear diffusion -- Entropy solution -- Orlicz–Sobolev space; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103631
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we are interested in the mathematical and numerical study of a reaction–diffusion system arising in the PDE-constrained optimization problems and image processing. The proposed model extends the recent work (Afraites et al., 2016) by taking L 1 data. We prove the existence and uniqueness of entropy solutions on the Orlicz–Sobolev space. Then, we present numerical experiments to illustrate the performance of the L 1 data choice and we discuss its efficiency compared to other image denoising algorithms.