Abstract:
In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J * u - u + G * (f (u)) - f (u) in Rd, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equation ut = Δ u + b ṡ ∇ (f (u)). In fact, we prove that solutions of the nonlocal equation converge to the solution of the usual convection-diffusion equation when we rescale the convolution kernels J and G appropriately. Finally we study the asymptotic behaviour of solutions as t → ∞ when f (u) = | u |q - 1 u with q > 1. We find the decay rate and the first-order term in the asymptotic regime. © 2007 Elsevier Inc. All rights reserved.
Registro:
Documento: |
Artículo
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Título: | A nonlocal convection-diffusion equation |
Autor: | Ignat, L.I.; Rossi, J.D. |
Filiación: | Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain Institute of Mathematics, the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania Departamento Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina
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Palabras clave: | Asymptotic behaviour; Convection-diffusion; Nonlocal diffusion |
Año: | 2007
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Volumen: | 251
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Número: | 2
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Página de inicio: | 399
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Página de fin: | 437
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DOI: |
http://dx.doi.org/10.1016/j.jfa.2007.07.013 |
Título revista: | Journal of Functional Analysis
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Título revista abreviado: | J. Funct. Anal.
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ISSN: | 00221236
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CODEN: | JFUAA
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PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00221236_v251_n2_p399_Ignat.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v251_n2_p399_Ignat |
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Citas:
---------- APA ----------
Ignat, L.I. & Rossi, J.D.
(2007)
. A nonlocal convection-diffusion equation. Journal of Functional Analysis, 251(2), 399-437.
http://dx.doi.org/10.1016/j.jfa.2007.07.013---------- CHICAGO ----------
Ignat, L.I., Rossi, J.D.
"A nonlocal convection-diffusion equation"
. Journal of Functional Analysis 251, no. 2
(2007) : 399-437.
http://dx.doi.org/10.1016/j.jfa.2007.07.013---------- MLA ----------
Ignat, L.I., Rossi, J.D.
"A nonlocal convection-diffusion equation"
. Journal of Functional Analysis, vol. 251, no. 2, 2007, pp. 399-437.
http://dx.doi.org/10.1016/j.jfa.2007.07.013---------- VANCOUVER ----------
Ignat, L.I., Rossi, J.D. A nonlocal convection-diffusion equation. J. Funct. Anal. 2007;251(2):399-437.
http://dx.doi.org/10.1016/j.jfa.2007.07.013