Well-posedness of an evolution problem with nonlocal diffusion. (February 2019)

• Record Type: Journal Article
• Authors: Galiano, Gonzalo
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 170
• Page End: 185
• Publication Date: 2019-02
• Subjects: Nonlocal diffusion -- Existence -- Uniqueness -- p-Laplacian -- Bilateral filter; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.06.013
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Hölder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics.