Wellposedness of a nonlocal nonlinear diffusion equation of image processing. (February 2017)

• Record Type: Journal Article
• Authors: Guidotti, Patrick; Shao, Yuanzhen
• Is Part Of: Nonlinear analysis. Volume 150(2017)
• Page Start: 114
• Page End: 137
• Publication Date: 2017-02
• Subjects: 35A01 -- 35A02 -- 35B40 -- 35K55 -- 35K65; Nonlinear nonlocal diffusion -- Perona–Malik equation -- Noise reduction -- Discontinuous initial data -- Well-posedness -- Stability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.11.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Existence and uniqueness of solutions to non-smooth initial data are established for a slight modification of the degenerate regularization of the well-known Perona–Malik equation first proposed in Guidotti and Lambers (2009). The results heavily rely on the choice of an appropriate functional setting inspired by a recent approach to degenerate parabolic equations via so-called singular Riemannian manifolds (Amann, 2013, 2016).