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Asymptotic behavior for a nonlocal diffusion equation on the half line
Finite mass solutions for a nonlocal inhomogeneous dispersal equation
1. | Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22. Santiago, Chile |
2. | Departamento de Matemáticas, Pontificia Universidad Católica de Chile, Santiago |
3. | Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271. La Laguna, Spain |
4. | Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, silla 170 Correo 3, Santiago |
References:
[1] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl., 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[2] |
C. Cortázar, J. Coville, M. Elgueta and S. Martínez, A non local inhomogeneous dispersal process, J. Diff. Eqns., 241 (2007), 332-358.
doi: 10.1016/j.jde.2007.06.002. |
[3] |
C. Cortázar, M. Elgueta, J. García-Melián and S. Martínez, Existence and asymptotic behavior of solutions to some inhomogeneous nonlocal diffusion problems, SIAM J. Math. Anal., 41 (2009), 2136-2164.
doi: 10.1137/090751682. |
[4] |
C. Cortázar, M. Elgueta, S. Martínez and J. Rossi, Random walks and the porous medium equation, Rev. Un. Mat. Argentina, 50 (2009), 149-155. |
[5] |
J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators, J. Differential Equations, 249 (2010), 2921-2953.
doi: 10.1016/j.jde.2010.07.003. |
[6] |
J. Coville, Harnack type inequality for positive solution of some integral equation, Ann. Mat. Pura Appl., (4) 191 (2012), 503-528.
doi: 10.1007/s10231-011-0193-2. |
[7] |
J. Coville, J. Dávila and S. Martínez, Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity, SIAM J. Math. Anal., 39 (2008), 1693-1709.
doi: 10.1137/060676854. |
[8] |
J. Coville, J. Dávila and S. Martínez, Pulsating fronts for nonlocal dispersion and KPP nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 179-223.
doi: 10.1016/j.anihpc.2012.07.005. |
[9] |
V. Hutson, S. Martínez, K. Mischaikow and G. T. Vickers, The evolution of dispersal, J. Math. Biol., 47 (2003), 483-517.
doi: 10.1007/s00285-003-0210-1. |
[10] |
K. Kawasaki and N. Shigesada, An integrodifference model for biological invasions in a periodically fragmented environment, Japan J. Indust. Appl. Math., 24 (2007), 3-15.
doi: 10.1007/BF03167504. |
[11] |
W. T. Li, J. W. Sun and F. Y. Yang, Approximate the Fokker-Planck equation by a class of nonlocal dispersal problems, Nonlinear Anal., 74 (2011), 3501-3509.
doi: 10.1016/j.na.2011.02.034. |
[12] |
W. T. Li, J. W. Sun and F. Y. Yang, Blow-up phenomena for nonlocal inhomogeneous diffusion problems, Turkish J. Math., 37 (2013), 466-482. |
[13] |
P. Michel, S. Mischler and B. Perthame, General relative entropy inequality: An illustration on growth models, J. Math. Pures Appl. (9), 84 (2005), 1235-1260.
doi: 10.1016/j.matpur.2005.04.001. |
[14] |
W. Shen and A. Zhang, Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats, J. Differential Equations, 249 (2010), 747-795.
doi: 10.1016/j.jde.2010.04.012. |
[15] |
W. Shen and A. Zhang, Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats, Proc. Amer. Math. Soc., 140 (2012), 1681-1696.
doi: 10.1090/S0002-9939-2011-11011-6. |
show all references
References:
[1] |
E. Chasseigne, M. Chaves and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl., 86 (2006), 271-291.
doi: 10.1016/j.matpur.2006.04.005. |
[2] |
C. Cortázar, J. Coville, M. Elgueta and S. Martínez, A non local inhomogeneous dispersal process, J. Diff. Eqns., 241 (2007), 332-358.
doi: 10.1016/j.jde.2007.06.002. |
[3] |
C. Cortázar, M. Elgueta, J. García-Melián and S. Martínez, Existence and asymptotic behavior of solutions to some inhomogeneous nonlocal diffusion problems, SIAM J. Math. Anal., 41 (2009), 2136-2164.
doi: 10.1137/090751682. |
[4] |
C. Cortázar, M. Elgueta, S. Martínez and J. Rossi, Random walks and the porous medium equation, Rev. Un. Mat. Argentina, 50 (2009), 149-155. |
[5] |
J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators, J. Differential Equations, 249 (2010), 2921-2953.
doi: 10.1016/j.jde.2010.07.003. |
[6] |
J. Coville, Harnack type inequality for positive solution of some integral equation, Ann. Mat. Pura Appl., (4) 191 (2012), 503-528.
doi: 10.1007/s10231-011-0193-2. |
[7] |
J. Coville, J. Dávila and S. Martínez, Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity, SIAM J. Math. Anal., 39 (2008), 1693-1709.
doi: 10.1137/060676854. |
[8] |
J. Coville, J. Dávila and S. Martínez, Pulsating fronts for nonlocal dispersion and KPP nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 179-223.
doi: 10.1016/j.anihpc.2012.07.005. |
[9] |
V. Hutson, S. Martínez, K. Mischaikow and G. T. Vickers, The evolution of dispersal, J. Math. Biol., 47 (2003), 483-517.
doi: 10.1007/s00285-003-0210-1. |
[10] |
K. Kawasaki and N. Shigesada, An integrodifference model for biological invasions in a periodically fragmented environment, Japan J. Indust. Appl. Math., 24 (2007), 3-15.
doi: 10.1007/BF03167504. |
[11] |
W. T. Li, J. W. Sun and F. Y. Yang, Approximate the Fokker-Planck equation by a class of nonlocal dispersal problems, Nonlinear Anal., 74 (2011), 3501-3509.
doi: 10.1016/j.na.2011.02.034. |
[12] |
W. T. Li, J. W. Sun and F. Y. Yang, Blow-up phenomena for nonlocal inhomogeneous diffusion problems, Turkish J. Math., 37 (2013), 466-482. |
[13] |
P. Michel, S. Mischler and B. Perthame, General relative entropy inequality: An illustration on growth models, J. Math. Pures Appl. (9), 84 (2005), 1235-1260.
doi: 10.1016/j.matpur.2005.04.001. |
[14] |
W. Shen and A. Zhang, Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats, J. Differential Equations, 249 (2010), 747-795.
doi: 10.1016/j.jde.2010.04.012. |
[15] |
W. Shen and A. Zhang, Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats, Proc. Amer. Math. Soc., 140 (2012), 1681-1696.
doi: 10.1090/S0002-9939-2011-11011-6. |
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