A class of nonlinear parabolic systems having standard growth and L1 data. (October 2022) - Atlas, Abdelghafour; Karami, Fahd; Meskine, Driss; Ouakrim, Youssef; Oubbih, Omar
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.