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On the limit of solutions for a reaction-di¤usion equation containing fractional Laplacians


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Title:
On the limit of solutions for a reaction-di¤usion equation containing fractional Laplacians
Authors:
Xu, Jiaohui
Caraballo, Tomas  
Valero, José  
Editor:
Plan S Approved
Department:
Departamentos de la UMH::Estadística, Matemáticas e Informática
Issue Date:
2023-12-20
URI:
https://hdl.handle.net/11000/32596
Abstract:
A kind of nonlocal reaction-di¤usion equations on an unbounded domain containing a frac- tional Laplacian operator is analyzed. To be precise, we prove the convergence of solutions of the equation governed by the fractional Laplacian to the solutions of the classical equation governed by the standard Laplacian, when the fractional parameter grows to 1. The existence of global attractors is investigated as well. The novelty of this paper is concerned with the convergence of solutions when the fractional parameter varies, which, as far as the authors are aware, seems to be the rst result of this kind of problems in the literature.
Keywords/Subjects:
Fractional Laplacian
Convergence of solutions
Global attractors
AMS subject classi cations
35R11, 35A15, 35B41, 35K65
Knowledge area:
CDU: Ciencias puras y naturales: Matemáticas
Type of document:
application/pdf
Access rights:
info:eu-repo/semantics/closedAccess
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
DOI:
https://doi.org/10.1007/s00245-023-10090-6
Appears in Collections:
Artículos Estadística, Matemáticas e Informática



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