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:
- Bates, P., Fife, P., Ren, X., Wang, X., Travelling waves in a convolution model for phase transitions (1997) Arch. Ration. Mech. Anal., 138, pp. 105-136
- Bates, P., Han, J., The Dirichlet boundary problem for a nonlocal Cahn-Hilliard equation (2005) J. Math. Anal. Appl., 311 (1), pp. 289-312
- Bates, P., Han, J., The Neumann boundary problem for a nonlocal Cahn-Hilliard equation (2005) J. Differential Equations, 212, pp. 235-277
- Chlebík, M., Fila, M., Some recent results on blow-up on the boundary for the heat equation (2000) Banach Center Publ., 52, pp. 61-71. , Evolution Equations: Existence, Regularity and Singularities. Warsaw, 1998, Polish Acad. Sci., Warsaw
- Cortazar, C., Elgueta, M., Rossi, J.D., A non-local diffusion equation whose solutions develop a free boundary (2005) Ann. Inst. H. Poincaré, 6 (2), pp. 269-281
- Chen, X., Existence, uniqueness and asymptotic stability of travelling waves in nonlocal evolution equations (1997) Adv. Differential Equations, 2, pp. 125-160
- Fife, P., Some nonclassical trends in parabolic and parabolic-like evolutions (2003) Trends in Nonlinear Analysis, pp. 153-191. , Springer, Berlin
- Fila, M., Filo, J., Blow-up on the boundary: A survey (1996) Banach Center Publ., 33, pp. 67-78. , Singularities and Differential Equations. Warsaw, 1993, Polish Acad. Sci., Warsaw
- 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
- Hu, B., Yin, H.M., The profile near blowup time for solution of the heat equation with a nonlinear boundary condition (1994) Trans. Amer. Math. Soc., 346 (1), pp. 117-135
- 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
- Wang, X., Metastability and stability of patterns in a convolution model for phase transitions (2002) J. Differential Equations, 183 (2), pp. 434-461
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