A class of nonlinear parabolic systems having standard growth and [formula omitted] data

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 L1 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 L1 data choice and we discuss its efficiency compared to other image denoising algorithms.