September  2016, 36(9): 5183-5199. doi: 10.3934/dcds.2016025

Asymptotic behavior of a nonlocal KPP equation with an almost periodic nonlinearity

1. 

35 River Drive S. Apt. 210, Jersey City, NJ 07310, United States

Received  December 2014 Revised  February 2016 Published  May 2016

We consider a space-inhomogeneous KPP equation with a nonlocal diffusion and an almost-periodic nonlinearity. By employing and adapting the theory of homogenization, we show that solutions of this equation asymptotically converge to its stationary states in regions of space separated by a front that is determined by a Hamilton-Jacobi variational inequality.
Citation: Yan Zhang. Asymptotic behavior of a nonlocal KPP equation with an almost periodic nonlinearity. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 5183-5199. doi: 10.3934/dcds.2016025
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Bull. Moscow State Univ. Ser. A: Math. Mech, 1 (1937), 1-25. Google Scholar

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Trans. Amer. Math. Soc., 2015, arXiv:1403.0166. doi: 10.1090/tran/6602.  Google Scholar

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P.-L. Lions, G. Papanicolaou and S. R. Varadhan, Homogenization of Hamilton-Jacobi equations,, Preliminary version., ().   Google Scholar

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show all references

References:
[1]

in Annales de l'Institut Henri Poincaré. Analyse non liné}aire, vol. 13, Elsevier, 1996, 293-317.  Google Scholar

[2]

in Proceedings of 10th International conference on mathematical finances sponcered by Daiwa securuty insurance, Dep. of Economics in Kyoto U, 2005. Google Scholar

[3]

Stochastic Processes and Applications To Mathematical Finance, (2007), 23-52, arXiv:1012.3108 doi: 10.1142/9789812770448_0002.  Google Scholar

[4]

Communications in Partial Differential Equations, 34 (2009), 617-624. arXiv:1012.4163 doi: 10.1080/03605300902963518.  Google Scholar

[5]

in Partial differential equations and related topics, Springer, 446 (1975), 5-49.  Google Scholar

[6]

Indiana University Mathematics Journal, 57 (2008), 213-246. doi: 10.1512/iumj.2008.57.3315.  Google Scholar

[7]

Methods and Applications of Analysis, 16 (2009), 321-340. arXiv:0903.4952. doi: 10.4310/MAA.2009.v16.n3.a4.  Google Scholar

[8]

Nonlinearity, 22 (2009), 2813-2844. doi: 10.1088/0951-7715/22/12/002.  Google Scholar

[9]

Journal of Differential Equations, 244 (2008), 3080-3118. doi: 10.1016/j.jde.2007.11.002.  Google Scholar

[10]

in Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 30 (2013), 179-223. doi: 10.1016/j.anihpc.2012.07.005.  Google Scholar

[11]

Bulletin of the American Mathematical Society, 27 (1992), 1-67. doi: 10.1090/S0273-0979-1992-00266-5.  Google Scholar

[12]

Archive for Rational Mechanics and Analysis, 105 (1989), 163-190. doi: 10.1007/BF00250835.  Google Scholar

[13]

Proc. Roy. Soc. Edinburgh Sect. A, 120 (1992), 245-265. doi: 10.1017/S0308210500032121.  Google Scholar

[14]

Indiana University mathematics journal, 38 (1989), 141-172. doi: 10.1512/iumj.1989.38.38007.  Google Scholar

[15]

Annals of Eugenics, 7 (1937), 355-369. doi: 10.1111/j.1469-1809.1937.tb02153.x.  Google Scholar

[16]

The Annals of Probability, 13 (1985), 639-675. doi: 10.1214/aop/1176992901.  Google Scholar

[17]

in International conference on differential equations, vol. 1, World Scientific, (2000), 600-605.  Google Scholar

[18]

Advances in Mathematical Sciences and Applications, 3 (1994), 191-218.  Google Scholar

[19]

Bull. Moscow State Univ. Ser. A: Math. Mech, 1 (1937), 1-25. Google Scholar

[20]

Trans. Amer. Math. Soc., 2015, arXiv:1403.0166. doi: 10.1090/tran/6602.  Google Scholar

[21]

P.-L. Lions, G. Papanicolaou and S. R. Varadhan, Homogenization of Hamilton-Jacobi equations,, Preliminary version., ().   Google Scholar

[22]

Nonlinearity, 7 (1994), 1-30. doi: 10.1088/0951-7715/7/1/001.  Google Scholar

[23]

Dynamical Systems, 13 (2005), 1235-1246. doi: 10.3934/dcds.2005.13.1235.  Google Scholar

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