Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

Related identifiers: doi: 10.1007/s0020501205192 
Subject: Mathematics  Analysis of PDEs  35R09, 45K05, 45M05

References
(16)
16 references, page 1 of 2
 1
 2
[1] Andreu, F.; Mazo´n, J.M.; Rossi, J.D.; Toledo, J., “Nonlocal Diffusion Problems”. American Mathematical Society. Mathematical Surveys and Monographs 2010. Vol. 165. ISBN10: 0821852302. ISBN13: 9780821852309.
[2] Bates, P.W.; Chmaj, A. An integrodifferential model for phase transitions: stationary solutions in higher dimensions. J. Statist. Phys. 95 (1999), no. 56, 11191139.
[3] Bates, P.W.; Chmaj, A. A discrete convolution model for phase transitions, Arch. Ration. Mech. Anal. 150 (1999), no. 4, 281305.
[4] Bates, P.W.; Zhao, G. Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal. J. Math. Anal. Appl. 332 (2007), no. 1, 428440.
[5] Br¨andle, C.; Chasseigne, E.; Ferreira, R. Unbounded solutions of the nonlocal heat equation. Commun. Pure Appl. Anal. 10 (2011), no. 6, 16631686.
[6] Br¨andle, C.; Quir´os, F.; V´azquez, J. L. Asymptotic behaviour of the porous media equation in domains with holes. Interfaces Free Bound. 9 (2007), no. 2, 211232.
[7] Carrillo, C.; Fife, P. Spatial effects in discrete generation population models. J. Math. Biol. 50 (2005), no. 2, 161188.
[8] Chasseigne, E.; Chaves, M.; Rossi, J.D. Asymptotic behavior for nonlocal diffusion equations. J. Math. Pures Appl. (9) 86 (2006), no. 3, 271291.
[9] Cort´azar, 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. 187 (2008), no. 1, 137156.
[10] Gilboa, G.; Osher, S. Nonlocal operators with application to image processing. Multiscale Model. Simul. 7 (2008), no. 3, 10051028.

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