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Preface: Special issue on dissipative systems and applications with emphasis on nonlocal or nonlinear diffusion problems
Asymptotic behavior for a nonlocal diffusion equation on the half line
1. | Departamento de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile, Chile |
2. | Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049-Madrid, Spain, Spain |
References:
[1] |
P. W. Bates and A. Chmaj, An integrodifferential model for phase transitions: Stationary solutions in higher dimensions, J. Statist. Phys., 95 (1999), 1119-1139.
doi: 10.1023/A:1004514803625. |
[2] |
P. W. Bates and A. Chmaj, A discrete convolution model for phase transitions, Arch. Ration. Mech. Anal., 150 (1999), 281-305.
doi: 10.1007/s002050050189. |
[3] |
P. W. Bates and G. Zhao, Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl., 332 (2007), 428-440.
doi: 10.1016/j.jmaa.2006.09.007. |
[4] |
C. Brändle, E. Chasseigne and R. Ferreira, Unbounded solutions of the nonlocal heat equation, Commun. Pure Appl. Anal., 10 (2011), 1663-1686.
doi: 10.3934/cpaa.2011.10.1663. |
[5] |
C. Carrillo and P. Fife, Spatial effects in discrete generation population models, J. Math. Biol., 50 (2005), 161-188.
doi: 10.1007/s00285-004-0284-4. |
[6] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl. (9), 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[7] |
C. Cortázar, M. Elgueta, F. Quirós and N. Wolanski, Asymptotic behavior for a nonlocal diffusion equation in domains with holes, Arch. Ration. Mech. Anal., 205 (2012), 673-697.
doi: 10.1007/s00205-012-0519-2. |
[8] |
C. Cortázar, M. Elgueta, J. D. Rossi and N. Wolanski, How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems, Arch. Ration. Mech. Anal., 187 (2008), 137-156.
doi: 10.1007/s00205-007-0062-8. |
[9] |
J. Duoandikoetxea and E. Zuazua, Moments, masses de Dirac et decomposition de fonctions, (French) [Moments, Dirac deltas and expansion of functions], C. R. Acad. Sci. Paris Ser. I Math., 315 (1992), 693-698. |
[10] |
P. Fife, Some nonclassical trends in parabolic and parabolic-like evolutions, in Trends in nonlinear analysis, (2003), 153-191. |
[11] |
G. Gilboa and S. Osher, Nonlocal operators with application to image processing, Multiscale Model. Simul., 7 (2008), 1005-1028.
doi: 10.1137/070698592. |
[12] |
L. A. Herraiz, A nonlinear parabolic problem in an exterior domain, J. Differential Equations, 142 (1998), 371-412.
doi: 10.1006/jdeq.1997.3358. |
[13] |
L. I. Ignat and J. D. Rossi, Refined asymptotic expansions for nonlocal diffusion equations, J. Evol. Equ., 8 (2008), 617-629.
doi: 10.1007/s00028-008-0372-9. |
[14] |
A. Wintner, On a class of fourier transforms, Amer. J. Math., 58 (1936), 45-90.
doi: 10.2307/2371058. |
show all references
References:
[1] |
P. W. Bates and A. Chmaj, An integrodifferential model for phase transitions: Stationary solutions in higher dimensions, J. Statist. Phys., 95 (1999), 1119-1139.
doi: 10.1023/A:1004514803625. |
[2] |
P. W. Bates and A. Chmaj, A discrete convolution model for phase transitions, Arch. Ration. Mech. Anal., 150 (1999), 281-305.
doi: 10.1007/s002050050189. |
[3] |
P. W. Bates and G. Zhao, Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl., 332 (2007), 428-440.
doi: 10.1016/j.jmaa.2006.09.007. |
[4] |
C. Brändle, E. Chasseigne and R. Ferreira, Unbounded solutions of the nonlocal heat equation, Commun. Pure Appl. Anal., 10 (2011), 1663-1686.
doi: 10.3934/cpaa.2011.10.1663. |
[5] |
C. Carrillo and P. Fife, Spatial effects in discrete generation population models, J. Math. Biol., 50 (2005), 161-188.
doi: 10.1007/s00285-004-0284-4. |
[6] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl. (9), 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[7] |
C. Cortázar, M. Elgueta, F. Quirós and N. Wolanski, Asymptotic behavior for a nonlocal diffusion equation in domains with holes, Arch. Ration. Mech. Anal., 205 (2012), 673-697.
doi: 10.1007/s00205-012-0519-2. |
[8] |
C. Cortázar, M. Elgueta, J. D. Rossi and N. Wolanski, How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems, Arch. Ration. Mech. Anal., 187 (2008), 137-156.
doi: 10.1007/s00205-007-0062-8. |
[9] |
J. Duoandikoetxea and E. Zuazua, Moments, masses de Dirac et decomposition de fonctions, (French) [Moments, Dirac deltas and expansion of functions], C. R. Acad. Sci. Paris Ser. I Math., 315 (1992), 693-698. |
[10] |
P. Fife, Some nonclassical trends in parabolic and parabolic-like evolutions, in Trends in nonlinear analysis, (2003), 153-191. |
[11] |
G. Gilboa and S. Osher, Nonlocal operators with application to image processing, Multiscale Model. Simul., 7 (2008), 1005-1028.
doi: 10.1137/070698592. |
[12] |
L. A. Herraiz, A nonlinear parabolic problem in an exterior domain, J. Differential Equations, 142 (1998), 371-412.
doi: 10.1006/jdeq.1997.3358. |
[13] |
L. I. Ignat and J. D. Rossi, Refined asymptotic expansions for nonlocal diffusion equations, J. Evol. Equ., 8 (2008), 617-629.
doi: 10.1007/s00028-008-0372-9. |
[14] |
A. Wintner, On a class of fourier transforms, Amer. J. Math., 58 (1936), 45-90.
doi: 10.2307/2371058. |
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