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: Ignat, L.I., Pinasco, D., Rossi, J.D., San Antolin, A.
Formato: JOUR
Acceso en línea: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 todo:paper_00217670_v122_n1_p375_Ignat
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spelling todo:paper_00217670_v122_n1_p375_Ignat2023-10-03T14:20:49Z Decay estimates for nonlinear nonlocal diffusion problems in the whole space Ignat, L.I. Pinasco, D. Rossi, J.D. San Antolin, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format JOUR
author Ignat, L.I.
Pinasco, D.
Rossi, J.D.
San Antolin, A.
spellingShingle Ignat, L.I.
Pinasco, D.
Rossi, J.D.
San Antolin, A.
Decay estimates for nonlinear nonlocal diffusion problems in the whole space
author_facet Ignat, L.I.
Pinasco, D.
Rossi, J.D.
San Antolin, A.
author_sort Ignat, L.I.
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
url http://hdl.handle.net/20.500.12110/paper_00217670_v122_n1_p375_Ignat
work_keys_str_mv AT ignatli decayestimatesfornonlinearnonlocaldiffusionproblemsinthewholespace
AT pinascod decayestimatesfornonlinearnonlocaldiffusionproblemsinthewholespace
AT rossijd decayestimatesfornonlinearnonlocaldiffusionproblemsinthewholespace
AT sanantolina decayestimatesfornonlinearnonlocaldiffusionproblemsinthewholespace
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