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Abstract:

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition. © 2006 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Boundary fluxes for nonlocal diffusion
Autor:Cortazar, C.; Elgueta, M.; Rossi, J.D.; Wolanski, N.
Filiación:Departamento de Matemática, Universidad Católica de Chile, Casilla 306, Correo 22 Santiago, Chile
Consejo Superior de Investigaciones Científicas (CSIC), Serrano 123, Madrid, Spain
Departamento de Matemática, FCEyN, UBA, 1428 Buenos Aires, Argentina
Palabras clave:Boundary value problems; Nonlocal diffusion
Año:2007
Volumen:234
Número:2
Página de inicio:360
Página de fin:390
DOI: http://dx.doi.org/10.1016/j.jde.2006.12.002
Título revista:Journal of Differential Equations
Título revista abreviado:J. Differ. Equ.
ISSN:00220396
CODEN:JDEQA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00220396_v234_n2_p360_Cortazar.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v234_n2_p360_Cortazar

Referencias:

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  • Bates, P., Han, J., The Neumann boundary problem for a nonlocal Cahn-Hilliard equation (2005) J. Differential Equations, 212, pp. 235-277
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  • Galaktionov, V.A., Vázquez, J.L., The problem of blow-up in nonlinear parabolic equations (2002) Discrete Contin. Dyn. Syst., 8 (2), pp. 399-433. , Current Developments in Partial Differential Equations. Temuco, 1999
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  • Lederman, C., Wolanski, N., Singular perturbation in a nonlocal diffusion problem (2006) Comm. Partial Differential Equations, 31 (1-3), pp. 195-241
  • Rial, D., Rossi, J.D., Blow-up results and localization of blow-up points in an N-dimensional smooth domain (1997) Duke Math. J., 88 (2), pp. 391-405
  • Samarski, A., Galaktionov, V.A., Kurdyunov, S.P., Mikailov, A.P., (1995) Blow-up in Quasilinear Parabolic Equations, , de Gruyter, Berlin
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Citas:

---------- APA ----------
Cortazar, C., Elgueta, M., Rossi, J.D. & Wolanski, N. (2007) . Boundary fluxes for nonlocal diffusion. Journal of Differential Equations, 234(2), 360-390.
http://dx.doi.org/10.1016/j.jde.2006.12.002
---------- CHICAGO ----------
Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N. "Boundary fluxes for nonlocal diffusion" . Journal of Differential Equations 234, no. 2 (2007) : 360-390.
http://dx.doi.org/10.1016/j.jde.2006.12.002
---------- MLA ----------
Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N. "Boundary fluxes for nonlocal diffusion" . Journal of Differential Equations, vol. 234, no. 2, 2007, pp. 360-390.
http://dx.doi.org/10.1016/j.jde.2006.12.002
---------- VANCOUVER ----------
Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N. Boundary fluxes for nonlocal diffusion. J. Differ. Equ. 2007;234(2):360-390.
http://dx.doi.org/10.1016/j.jde.2006.12.002