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Abstract:

We present a model for nonlocal diffusion with Neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary. We study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero. We prove that the solutions of this family of problems converge to a solution of the heat equation with Neumann boundary conditions. © 2007 Springer-Verlag.

Registro:

Documento: Artículo
Título:How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
Autor:Cortazar, C.; Elgueta, M.; Rossi, J.D.; Wolanski, N.
Filiación:Departamento de Matemática, Universidad Catolica de Chile, Casilla 306, Correo 22, Santiago, Chile
Departamento de Matemática, FCEyN, Pab I, (1428) Buenos Aires, Argentina
Año:2008
Volumen:187
Número:1
Página de inicio:137
Página de fin:156
DOI: http://dx.doi.org/10.1007/s00205-007-0062-8
Título revista:Archive for Rational Mechanics and Analysis
Título revista abreviado:Arch. Ration. Mech. Anal.
ISSN:00039527
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00039527_v187_n1_p137_Cortazar

Referencias:

  • Bates, P., Chmaj, A., An integrodifferential model for phase transitions: Stationary solutions in higher dimensions (1999) J. Statist. Phys., 95, pp. 1119-1139
  • Bates, P., Chmaj, A., A discrete convolution model for phase transitions (1999) Arch. Ration Mech. Anal., 150, pp. 281-305
  • Bates, P., Fife, P., Ren, X., Wang, X., Traveling 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, 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
  • Carrillo, C., Fife, P., Spatial effects in discrete generation population models (2005) J. Math. Biol., 50, pp. 161-188
  • Cortazar, C., Elgueta, M., Rossi, J.D., A nonlocal diffusion equation whose solutions develop a free boundary (2005) Ann. Henri Poincaré, 6, pp. 269-281
  • Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N., Boundary fluxes for nonlocal diffusion J. Differential Equations, , To appear in
  • Chen, X., Existence, uniqueness and asymptotic stability of traveling 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, , Springer, Berlin
  • Friedman, A., (1964) Partial Differential Equations of Parabolic Type, , Prentice-Hall Englewood Cliffs, NJ
  • Lederman, C., Wolanski, N., Singular perturbation in a nonlocal diffusion problem (2006) Comm. Partial Differential Equations., 31, pp. 195-241
  • Wang, X., Metastability and stability of patterns in a convolution model for phase transitions (2002) J. Differential Equations., 183, pp. 434-461
  • Zhang, L., Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks (2004) J. Differential Equations, 197, pp. 162-196

Citas:

---------- APA ----------
Cortazar, C., Elgueta, M., Rossi, J.D. & Wolanski, N. (2008) . How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems. Archive for Rational Mechanics and Analysis, 187(1), 137-156.
http://dx.doi.org/10.1007/s00205-007-0062-8
---------- CHICAGO ----------
Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N. "How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems" . Archive for Rational Mechanics and Analysis 187, no. 1 (2008) : 137-156.
http://dx.doi.org/10.1007/s00205-007-0062-8
---------- MLA ----------
Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N. "How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems" . Archive for Rational Mechanics and Analysis, vol. 187, no. 1, 2008, pp. 137-156.
http://dx.doi.org/10.1007/s00205-007-0062-8
---------- VANCOUVER ----------
Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N. How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems. Arch. Ration. Mech. Anal. 2008;187(1):137-156.
http://dx.doi.org/10.1007/s00205-007-0062-8