Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum. © 2010 American Mathematical Society.

Registro:

Documento: Artículo
Título:Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case
Autor:Terra, J.; Wolanski, N.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Boundary value problems; Nonlocal diffusion
Año:2011
Volumen:139
Número:4
Página de inicio:1421
Página de fin:1432
DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10612-3
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v139_n4_p1421_Terra

Referencias:

  • Bates, P., Chmaj, A., An integrodifferential model for phase transitions: Stationary solutions in higher dimensions (1999) J.Statistical Phys., 95, pp. 1119-1139. , MR1712445 (2000j:82020)
  • Bates, P., Chmaj, A., A discrete convolution model for phase transitions (1999) Arch.Rat.Mech.Anal., 150, pp. 281-305. , MR1741258 (2001c:82026)
  • Bates, P., Fife, P., Ren, X., Wang, X., Travelling waves in a convolution model for phase transitions (1997) Arch.Rat.Mech.Anal., 138, pp. 105-136. , MR1463804 (98f:45004)
  • Carrillo, C., Fife, P., Spatial effects in discrete generation population models (2005) Journal of Mathematical Biology, 50 (2), pp. 161-188. , DOI 10.1007/s00285-004-0284-4
  • Chasseigne, E., Chaves, M., Rossi, J.D., Asymptotic behavior for nonlocal diffusion equations (2006) Journal des Mathematiques Pures et Appliquees, 86 (3), pp. 271-291. , DOI 10.1016/j.matpur.2006.04.005, PII S0021782406000559
  • Cortazar, C., Elgueta, M., Quiros, F., Wolanski, N., Large Time Behavior of the Solution to the Dirichlet Problem for a Nonlocal Diffusion Equation in an Exterior Domain, , in preparation
  • Cortazar, C., Elgueta, M., Rossi, J.D., Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions (2009) Israel Journal of Mathematics, 170 (1), pp. 53-60. , MR2506317 (2010e:35197)
  • Cortazar, C., Elgueta, M., Rossi, J.D., Wolanski, N., How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems (2008) Arch.Rat.Mech.Anal., 187 (1), pp. 137-156. , MR2358337 (2008k:35261)
  • Fife, P., Some nonclassical trends in parabolic and parabolic-like evolutions (2003) Trends in Nonlinear Analysis, pp. 153-191. , Springer, Berlin .MR1999098 (2004h:35100)
  • Gilboa, G., Osher, S., Nonlocal operators with application to image processing (2008) Multiscale Model.Simul., 7 (3), pp. 1005-1028. , MR2480109 (2010b:94006)
  • Grafakos, L., Classical fourier analysis (2008) Graduate Texts in Mathematics, 249. , Second edition.Springer, New York MR2445437
  • Herraiz, L., Asymptotic behaviour of solutions of some semilinear parabolic problems (1999) Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, 16 (1), pp. 49-105
  • Ignat, L.I., Rossi, J.D., Refined asymptotic expansions for nonlocal diffusion equations (2008) J.Evolution Equations., 8, pp. 617-629. , MR2460931 (2009j:45001)
  • Kamin, S., Peletier, L.A., Large time behavior of solutions of the heat equation with absorption (1985) Anal.Scuola.Norm.Sup.Pisa Serie 4, 12, pp. 393-408. , MR837255 (87h:35140)
  • Kamin, S., Ughi, M., On the behaviour as t → ∞ of the solutions of the Cauchy problem for certain nonlinear parabolic equations (1997) J.Math.Anal.Appl., 128, pp. 456-469. , MR917378 (89m:35029)
  • Lederman, C., Wolanski, N., Singular perturbation in a nonlocal diffusion problem (2006) Communications in Partial Differential Equations, 31 (2), pp. 195-241. , DOI 10.1080/03605300500358111, PII M705432860742
  • Pazoto, A.F., Rossi, J.D., Asymptotic behaviour for a semilinear nonlocal equation (2007) Asymptotic Analysis, 52 (1-2), pp. 143-155
  • Terra, J., Wolanski, N., Large Time Behavior for a Nonlocal Diffusion Equation with Absorption and Bounded Initial Data, , submitted
  • Zhang, L., Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks (2004) Journal of Differential Equations, 197 (1), pp. 162-196. , DOI 10.1016/S0022-0396(03)00170-0

Citas:

---------- APA ----------
Terra, J. & Wolanski, N. (2011) . Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case. Proceedings of the American Mathematical Society, 139(4), 1421-1432.
http://dx.doi.org/10.1090/S0002-9939-2010-10612-3
---------- CHICAGO ----------
Terra, J., Wolanski, N. "Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case" . Proceedings of the American Mathematical Society 139, no. 4 (2011) : 1421-1432.
http://dx.doi.org/10.1090/S0002-9939-2010-10612-3
---------- MLA ----------
Terra, J., Wolanski, N. "Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case" . Proceedings of the American Mathematical Society, vol. 139, no. 4, 2011, pp. 1421-1432.
http://dx.doi.org/10.1090/S0002-9939-2010-10612-3
---------- VANCOUVER ----------
Terra, J., Wolanski, N. Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data. The supercritical case. Proc. Am. Math. Soc. 2011;139(4):1421-1432.
http://dx.doi.org/10.1090/S0002-9939-2010-10612-3