Decay estimates for nonlinear nonlocal diffusion problems in the whole space

In this paper, we obtain bounds for the decay rate in the Lr (ℝd)-norm for the solutions of a nonlocal and nonlinear evolution equation, namely, (Formula presented.). We consider a kernel of the form K(x, y) = ψ(y-a(x)) + ψ(x-a(y)), where ψ is a bounded, nonnegative function supported in the unit ba...

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Autores principales: Pinasco, Damián, Rossi, Julio Daniel
Publicado: 2014
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217670_v122_n1_p375_Ignat
http://hdl.handle.net/20.500.12110/paper_00217670_v122_n1_p375_Ignat
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00217670_v122_n1_p375_Ignat
record_format dspace
spelling paper:paper_00217670_v122_n1_p375_Ignat2023-06-08T14:42:04Z Decay estimates for nonlinear nonlocal diffusion problems in the whole space Pinasco, Damián Rossi, Julio Daniel In this paper, we obtain bounds for the decay rate in the Lr (ℝd)-norm for the solutions of a nonlocal and nonlinear evolution equation, namely, (Formula presented.). We consider a kernel of the form K(x, y) = ψ(y-a(x)) + ψ(x-a(y)), where ψ is a bounded, nonnegative function supported in the unit ball and a is a linear function a(x) = Ax. To obtain the decay rates, we derive lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form (Formula presented.). The upper and lower bounds that we obtain are sharp and provide an explicit expression for the first eigenvalue in the whole space ℝd: (Formula presented.) Moreover, we deal with the p = ∞ eigenvalue problem, studying the limit of λ1,p 1/p as p→∞. © 2014 Hebrew University Magnes Press. Fil:Pinasco, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217670_v122_n1_p375_Ignat http://hdl.handle.net/20.500.12110/paper_00217670_v122_n1_p375_Ignat
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this paper, we obtain bounds for the decay rate in the Lr (ℝd)-norm for the solutions of a nonlocal and nonlinear evolution equation, namely, (Formula presented.). We consider a kernel of the form K(x, y) = ψ(y-a(x)) + ψ(x-a(y)), where ψ is a bounded, nonnegative function supported in the unit ball and a is a linear function a(x) = Ax. To obtain the decay rates, we derive lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form (Formula presented.). The upper and lower bounds that we obtain are sharp and provide an explicit expression for the first eigenvalue in the whole space ℝd: (Formula presented.) Moreover, we deal with the p = ∞ eigenvalue problem, studying the limit of λ1,p 1/p as p→∞. © 2014 Hebrew University Magnes Press.
author Pinasco, Damián
Rossi, Julio Daniel
spellingShingle Pinasco, Damián
Rossi, Julio Daniel
Decay estimates for nonlinear nonlocal diffusion problems in the whole space
author_facet Pinasco, Damián
Rossi, Julio Daniel
author_sort Pinasco, Damián
title Decay estimates for nonlinear nonlocal diffusion problems in the whole space
title_short Decay estimates for nonlinear nonlocal diffusion problems in the whole space
title_full Decay estimates for nonlinear nonlocal diffusion problems in the whole space
title_fullStr Decay estimates for nonlinear nonlocal diffusion problems in the whole space
title_full_unstemmed Decay estimates for nonlinear nonlocal diffusion problems in the whole space
title_sort decay estimates for nonlinear nonlocal diffusion problems in the whole space
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217670_v122_n1_p375_Ignat
http://hdl.handle.net/20.500.12110/paper_00217670_v122_n1_p375_Ignat
work_keys_str_mv AT pinascodamian decayestimatesfornonlinearnonlocaldiffusionproblemsinthewholespace
AT rossijuliodaniel decayestimatesfornonlinearnonlocaldiffusionproblemsinthewholespace
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