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Linear non-local diffusion problems in metric measure spaces

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Rodríguez Bernal, Aníbal and Sastre Gómez, S. (2016) Linear non-local diffusion problems in metric measure spaces. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 146 (1). pp. 833-863. ISSN 03082105

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Official URL: https://arxiv.org/pdf/1412.5438v1.pdf



Abstract

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.


Item Type:Article
Uncontrolled Keywords:Linear problem; Metric measure spaces; Non-local diffusion
Subjects:Sciences > Mathematics > Topology
ID Code:39255
Deposited On:07 Oct 2016 12:05
Last Modified:12 Dec 2018 15:06

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