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Combining linear and nonlinear diffusion


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Author: Delgado Delgado, Manuel
López Gómez, Julián
Suárez Fernández, Antonio
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2004-08
Published in: Advanced Nonlinear Studies, 4 (3), 273-287.
Document type: Article
Abstract: In this paper we study a generalized porous medium equation where the diffusion rate, say m(x) —spatially heterogeneous—, is assumed to be linear, m = 1, on a piece of the support domain, Ω1, and slow nonlinear, m(x) > 1, in its complement, Ωm := Ω \ Ω¯1. Most precisely, we characterize the existence of positive solutions and construct the corresponding global bifurcation diagram as one of the parameters of the model changes, showing that a continuous transition occurs between the diagrams of the completely linear case (Ω = Ω1) and of the completely nonlinear case (Ωm = Ω). As a result, the effect of a localized slow diffusion rate with varying support is completely characterized. Our analysis is imperative in order to design porous media multi-components systems with changing diffusion rates.
Cite: Delgado Delgado, M., López Gómez, J. y Suárez Fernández, A. (2004). Combining linear and nonlinear diffusion. Advanced Nonlinear Studies, 4 (3), 273-287.
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DOI: 10.1515/ans-2004-0303

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