Decay bounds for nonlocal evolution equations in Orlicz spaces

We show decay bounds of the form ∫Rd ϕ(u(x,t))dx≤Ct-μ for integrable and bounded solutions to the nonlocal evolution equation ut(x,t)= ∫Rd J(x,y)G(u(y,t)-u(x,t))(u(y,t)-u(x,t))dy+f(u(x,t)). Here G is a nonnegative and even function, and f verifies f(ξ)ξ ≤ 0 for all ξ≥0. We remark that G is not assum...

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Guardado en:
Detalles Bibliográficos
Publicado: 2016
Materias:
Energy methods
Nonlocal diffusion
Orlicz space
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20088752_v7_n2_p261_Kaufmann
http://hdl.handle.net/20.500.12110/paper_20088752_v7_n2_p261_Kaufmann
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_20088752_v7_n2_p261_Kaufmann
record_format dspace
spelling paper:paper_20088752_v7_n2_p261_Kaufmann2023-06-08T16:32:57Z Decay bounds for nonlocal evolution equations in Orlicz spaces Energy methods Nonlocal diffusion Orlicz space We show decay bounds of the form ∫Rd ϕ(u(x,t))dx≤Ct-μ for integrable and bounded solutions to the nonlocal evolution equation ut(x,t)= ∫Rd J(x,y)G(u(y,t)-u(x,t))(u(y,t)-u(x,t))dy+f(u(x,t)). Here G is a nonnegative and even function, and f verifies f(ξ)ξ ≤ 0 for all ξ≥0. We remark that G is not assumed to be homogeneous. The function ϕ and the exponent μ depend on G via adequate hypotheses, while J is a nonnegative kernel satisfying suitable assumptions. © 2016 Tusi Mathematical Research Group. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20088752_v7_n2_p261_Kaufmann http://hdl.handle.net/20.500.12110/paper_20088752_v7_n2_p261_Kaufmann
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Energy methods
Nonlocal diffusion
Orlicz space
spellingShingle Energy methods
Nonlocal diffusion
Orlicz space
Decay bounds for nonlocal evolution equations in Orlicz spaces
topic_facet Energy methods
Nonlocal diffusion
Orlicz space
description We show decay bounds of the form ∫Rd ϕ(u(x,t))dx≤Ct-μ for integrable and bounded solutions to the nonlocal evolution equation ut(x,t)= ∫Rd J(x,y)G(u(y,t)-u(x,t))(u(y,t)-u(x,t))dy+f(u(x,t)). Here G is a nonnegative and even function, and f verifies f(ξ)ξ ≤ 0 for all ξ≥0. We remark that G is not assumed to be homogeneous. The function ϕ and the exponent μ depend on G via adequate hypotheses, while J is a nonnegative kernel satisfying suitable assumptions. © 2016 Tusi Mathematical Research Group.
title Decay bounds for nonlocal evolution equations in Orlicz spaces
title_short Decay bounds for nonlocal evolution equations in Orlicz spaces
title_full Decay bounds for nonlocal evolution equations in Orlicz spaces
title_fullStr Decay bounds for nonlocal evolution equations in Orlicz spaces
title_full_unstemmed Decay bounds for nonlocal evolution equations in Orlicz spaces
title_sort decay bounds for nonlocal evolution equations in orlicz spaces
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20088752_v7_n2_p261_Kaufmann
http://hdl.handle.net/20.500.12110/paper_20088752_v7_n2_p261_Kaufmann
_version_ 1768545713526931456

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