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Abstract:

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.

Registro:

Documento: Artículo
Título:Decay bounds for nonlocal evolution equations in Orlicz spaces
Autor:Kaufmann, U.; Rossi, J.D.; Vidal, R.
Filiación:FaMAF, Universidad Nacional de Cordoba, Cordoba, 5000, Argentina
CONICET and Depto. de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab 1, Buenos Aires, 1428, Argentina
Palabras clave:Energy methods; Nonlocal diffusion; Orlicz space
Año:2016
Volumen:7
Número:2
Página de inicio:261
Página de fin:269
DOI: http://dx.doi.org/10.1215/20088752-3475634
Título revista:Annals of Functional Analysis
Título revista abreviado:Ann. Funct. Anal.
ISSN:20088752
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_20088752_v7_n2_p261_Kaufmann

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Citas:

---------- APA ----------
Kaufmann, U., Rossi, J.D. & Vidal, R. (2016) . Decay bounds for nonlocal evolution equations in Orlicz spaces. Annals of Functional Analysis, 7(2), 261-269.
http://dx.doi.org/10.1215/20088752-3475634
---------- CHICAGO ----------
Kaufmann, U., Rossi, J.D., Vidal, R. "Decay bounds for nonlocal evolution equations in Orlicz spaces" . Annals of Functional Analysis 7, no. 2 (2016) : 261-269.
http://dx.doi.org/10.1215/20088752-3475634
---------- MLA ----------
Kaufmann, U., Rossi, J.D., Vidal, R. "Decay bounds for nonlocal evolution equations in Orlicz spaces" . Annals of Functional Analysis, vol. 7, no. 2, 2016, pp. 261-269.
http://dx.doi.org/10.1215/20088752-3475634
---------- VANCOUVER ----------
Kaufmann, U., Rossi, J.D., Vidal, R. Decay bounds for nonlocal evolution equations in Orlicz spaces. Ann. Funct. Anal. 2016;7(2):261-269.
http://dx.doi.org/10.1215/20088752-3475634