-
Previous Article
Adaptation and migration of a population between patches
- DCDS-B Home
- This Issue
-
Next Article
Robustness of Morphogen gradients with "bucket brigade" transport through membrane-associated non-receptors
Multidimensional stability of planar traveling waves for an integrodifference model
1. | Dept. of Mathematics and Statistics, Georgetown University, Washington DC 20057, United States |
2. | Mathematical Sciences Center, Tsinghua University, Beijing 100084, China |
References:
[1] |
O. Diekmann and H. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Anal., 2 (1978), 721-737.
doi: 10.1016/0362-546X(78)90015-9. |
[2] |
P. Fife and J. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361. |
[3] |
R. Gardner and K. Zumbrun, The gap lemma and geometric criteria for instability of viscous shock profiles, Comm. Pure Appl. Math., 51 (1998), 797-855.
doi: 10.1002/(SICI)1097-0312(199807)51:7<797::AID-CPA3>3.0.CO;2-1. |
[4] |
M. Gil', "Difference Equations in Normed Spaces. Stability and Oscillations," North-Holland Mathematics Studies, 206, Elsevier Science B.V., Amsterdam, 2007. |
[5] |
J. Goodman, Stability of viscous scalar shock fronts in several dimensions, Trans. Amer. Math. Soc., 311 (1989), 683-695.
doi: 10.2307/2001146. |
[6] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[7] |
S. Hsu and X. Zhao, Spreading speeds and traveling waves for nonmonotone integrodifference equations, SIAM J. Math. Anal., 40 (2008), 776-789.
doi: 10.1137/070703016. |
[8] |
T. Kapitula, Multidimensional stability of planar travelling waves, Trans. Amer. Math. Soc., 349 (1997), 257-269.
doi: 10.1090/S0002-9947-97-01668-1. |
[9] |
M. Kot and W. Schaffer, Discrete-time growth-dispersal models, Math. Biosci., 80 (1986), 109-136.
doi: 10.1016/0025-5564(86)90069-6. |
[10] |
M. Kot, Discrete-time travelling waves: Ecological examples, J. Math. Biol., 30 (1992), 413-436.
doi: 10.1007/BF00173295. |
[11] |
M. Kot, M. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms, Ecology, 77 (1996), 2027-2042. |
[12] |
C. Levermore and J. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation. II, Comm. Partial Differential Equations, 17 (1992), 1901-1924.
doi: 10.1080/03605309208820908. |
[13] |
B. Li, M. Lewis and H. Weinberger, Existence of traveling waves for integral recursions with nonmonotone growth functions, J. Math. Biol., 58 (2009), 323-338.
doi: 10.1007/s00285-008-0175-1. |
[14] |
G. Lin and W. Li, Spreading speeds and traveling wavefronts for second order integrodifference equations, J. Math. Anal. Appl., 361 (2010), 520-532.
doi: 10.1016/j.jmaa.2009.07.035. |
[15] |
G. Lin, W. Li and S. Ruan, Asymptotic stability of monostable wavefronts in disctrete-time integral recursions, Sci. China Math., 53 (2010), 1185-1194.
doi: 10.1007/s11425-009-0123-6. |
[16] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. I. Monotone initial data, SIAM J. Math. Anal., 13 (1982), 913-937.
doi: 10.1137/0513064. |
[17] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. II. Initial data with compact support, SIAM J. Math. Anal., 13 (1982), 938-953.
doi: 10.1137/0513065. |
[18] |
R. Lui, Existence and stability of travelling wave solutions of a nonlinear integral operator, J. Math. Biol., 16 (1982/83), 199-220.
doi: 10.1007/BF00276502. |
[19] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. III. Heterozygote inferior case, SIAM J. Math. Anal., 16 (1985), 1180-1206.
doi: 10.1137/0516087. |
[20] |
J. Miller and H. Zeng, Stability of travelling waves for systems of nonlinear integral recursions in spatial population biology, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 895-925.
doi: 10.3934/dcdsb.2011.16.895. |
[21] |
M. Neubert, M. Kot and M. Lewis, Dispersal and pattern-formation in a discrete-time predator-prey model, Theoretical Population Biology, 48 (1995), 7-43. |
[22] |
D. Sattinger, On the stability of waves of nonlinear parabolic systems, Advances in Math., 22 (1976), 312-355. |
[23] |
H. Weinberger, Asymptotic behavior of a model in population genetics, in "Nonlinear Partial Differential Equations and Applications" (Proc. Special Sem., Indiana Univ., Bloomington, Ind., 1976-1977), Lecture Notes in Math., Vol. 648, Springer, Berlin, (1978), 47-96. |
[24] |
H. Weinberger, Long-time behavior of a class of biological models, SIAM J. Math. Anal., 13 (1982), 353-396.
doi: 10.1137/0513028. |
[25] |
J. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation. I, Comm. Partial Differential Equations, 17 (1992), 1889-1899.
doi: 10.1080/03605309208820907. |
[26] |
K. Zumbrun and P. Howard, Pointwise semigroup methods and stability of viscous shock waves, Indiana Univ. Math. J., 47 (1998), 741-871.
doi: 10.1512/iumj.1998.47.1604. |
show all references
References:
[1] |
O. Diekmann and H. Kaper, On the bounded solutions of a nonlinear convolution equation, Nonlinear Anal., 2 (1978), 721-737.
doi: 10.1016/0362-546X(78)90015-9. |
[2] |
P. Fife and J. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361. |
[3] |
R. Gardner and K. Zumbrun, The gap lemma and geometric criteria for instability of viscous shock profiles, Comm. Pure Appl. Math., 51 (1998), 797-855.
doi: 10.1002/(SICI)1097-0312(199807)51:7<797::AID-CPA3>3.0.CO;2-1. |
[4] |
M. Gil', "Difference Equations in Normed Spaces. Stability and Oscillations," North-Holland Mathematics Studies, 206, Elsevier Science B.V., Amsterdam, 2007. |
[5] |
J. Goodman, Stability of viscous scalar shock fronts in several dimensions, Trans. Amer. Math. Soc., 311 (1989), 683-695.
doi: 10.2307/2001146. |
[6] |
D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin-New York, 1981. |
[7] |
S. Hsu and X. Zhao, Spreading speeds and traveling waves for nonmonotone integrodifference equations, SIAM J. Math. Anal., 40 (2008), 776-789.
doi: 10.1137/070703016. |
[8] |
T. Kapitula, Multidimensional stability of planar travelling waves, Trans. Amer. Math. Soc., 349 (1997), 257-269.
doi: 10.1090/S0002-9947-97-01668-1. |
[9] |
M. Kot and W. Schaffer, Discrete-time growth-dispersal models, Math. Biosci., 80 (1986), 109-136.
doi: 10.1016/0025-5564(86)90069-6. |
[10] |
M. Kot, Discrete-time travelling waves: Ecological examples, J. Math. Biol., 30 (1992), 413-436.
doi: 10.1007/BF00173295. |
[11] |
M. Kot, M. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms, Ecology, 77 (1996), 2027-2042. |
[12] |
C. Levermore and J. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation. II, Comm. Partial Differential Equations, 17 (1992), 1901-1924.
doi: 10.1080/03605309208820908. |
[13] |
B. Li, M. Lewis and H. Weinberger, Existence of traveling waves for integral recursions with nonmonotone growth functions, J. Math. Biol., 58 (2009), 323-338.
doi: 10.1007/s00285-008-0175-1. |
[14] |
G. Lin and W. Li, Spreading speeds and traveling wavefronts for second order integrodifference equations, J. Math. Anal. Appl., 361 (2010), 520-532.
doi: 10.1016/j.jmaa.2009.07.035. |
[15] |
G. Lin, W. Li and S. Ruan, Asymptotic stability of monostable wavefronts in disctrete-time integral recursions, Sci. China Math., 53 (2010), 1185-1194.
doi: 10.1007/s11425-009-0123-6. |
[16] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. I. Monotone initial data, SIAM J. Math. Anal., 13 (1982), 913-937.
doi: 10.1137/0513064. |
[17] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. II. Initial data with compact support, SIAM J. Math. Anal., 13 (1982), 938-953.
doi: 10.1137/0513065. |
[18] |
R. Lui, Existence and stability of travelling wave solutions of a nonlinear integral operator, J. Math. Biol., 16 (1982/83), 199-220.
doi: 10.1007/BF00276502. |
[19] |
R. Lui, A nonlinear integral operator arising from a model in population genetics. III. Heterozygote inferior case, SIAM J. Math. Anal., 16 (1985), 1180-1206.
doi: 10.1137/0516087. |
[20] |
J. Miller and H. Zeng, Stability of travelling waves for systems of nonlinear integral recursions in spatial population biology, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 895-925.
doi: 10.3934/dcdsb.2011.16.895. |
[21] |
M. Neubert, M. Kot and M. Lewis, Dispersal and pattern-formation in a discrete-time predator-prey model, Theoretical Population Biology, 48 (1995), 7-43. |
[22] |
D. Sattinger, On the stability of waves of nonlinear parabolic systems, Advances in Math., 22 (1976), 312-355. |
[23] |
H. Weinberger, Asymptotic behavior of a model in population genetics, in "Nonlinear Partial Differential Equations and Applications" (Proc. Special Sem., Indiana Univ., Bloomington, Ind., 1976-1977), Lecture Notes in Math., Vol. 648, Springer, Berlin, (1978), 47-96. |
[24] |
H. Weinberger, Long-time behavior of a class of biological models, SIAM J. Math. Anal., 13 (1982), 353-396.
doi: 10.1137/0513028. |
[25] |
J. Xin, Multidimensional stability of traveling waves in a bistable reaction-diffusion equation. I, Comm. Partial Differential Equations, 17 (1992), 1889-1899.
doi: 10.1080/03605309208820907. |
[26] |
K. Zumbrun and P. Howard, Pointwise semigroup methods and stability of viscous shock waves, Indiana Univ. Math. J., 47 (1998), 741-871.
doi: 10.1512/iumj.1998.47.1604. |
[1] |
Adèle Bourgeois, Victor LeBlanc, Frithjof Lutscher. Dynamical stabilization and traveling waves in integrodifference equations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 3029-3045. doi: 10.3934/dcdss.2020117 |
[2] |
Luyi Ma, Hong-Tao Niu, Zhi-Cheng Wang. Global asymptotic stability of traveling waves to the Allen-Cahn equation with a fractional Laplacian. Communications on Pure and Applied Analysis, 2019, 18 (5) : 2457-2472. doi: 10.3934/cpaa.2019111 |
[3] |
Grégory Faye. Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2473-2496. doi: 10.3934/dcds.2016.36.2473 |
[4] |
Aslihan Demirkaya, Milena Stanislavova. Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 197-209. doi: 10.3934/dcdsb.2018097 |
[5] |
Hua Chen, Ling-Jun Wang. A perturbation approach for the transverse spectral stability of small periodic traveling waves of the ZK equation. Kinetic and Related Models, 2012, 5 (2) : 261-281. doi: 10.3934/krm.2012.5.261 |
[6] |
Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure and Applied Analysis, 2011, 10 (1) : 141-160. doi: 10.3934/cpaa.2011.10.141 |
[7] |
Guo Lin, Shuxia Pan. Periodic traveling wave solutions of periodic integrodifference systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3005-3031. doi: 10.3934/dcdsb.2020049 |
[8] |
Joseph Thirouin. Classification of traveling waves for a quadratic Szegő equation. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3099-3122. doi: 10.3934/dcds.2019128 |
[9] |
Zhaosheng Feng. Traveling waves to a reaction-diffusion equation. Conference Publications, 2007, 2007 (Special) : 382-390. doi: 10.3934/proc.2007.2007.382 |
[10] |
Yaping Wu, Niannian Yan. Stability of traveling waves for autocatalytic reaction systems with strong decay. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1601-1633. doi: 10.3934/dcdsb.2017033 |
[11] |
Fengxin Chen. Stability and uniqueness of traveling waves for system of nonlocal evolution equations with bistable nonlinearity. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 659-673. doi: 10.3934/dcds.2009.24.659 |
[12] |
Grigori Chapiro, Lucas Furtado, Dan Marchesin, Stephen Schecter. Stability of interacting traveling waves in reaction-convection-diffusion systems. Conference Publications, 2015, 2015 (special) : 258-266. doi: 10.3934/proc.2015.0258 |
[13] |
Je-Chiang Tsai. Global exponential stability of traveling waves in monotone bistable systems. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 601-623. doi: 10.3934/dcds.2008.21.601 |
[14] |
Zigen Ouyang, Chunhua Ou. Global stability and convergence rate of traveling waves for a nonlocal model in periodic media. Discrete and Continuous Dynamical Systems - B, 2012, 17 (3) : 993-1007. doi: 10.3934/dcdsb.2012.17.993 |
[15] |
Judith R. Miller, Huihui Zeng. Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 895-925. doi: 10.3934/dcdsb.2011.16.895 |
[16] |
Tong Li, Jeungeun Park. Stability of traveling waves of models for image processing with non-convex nonlinearity. Communications on Pure and Applied Analysis, 2018, 17 (3) : 959-985. doi: 10.3934/cpaa.2018047 |
[17] |
Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, 2021, 29 (4) : 2599-2618. doi: 10.3934/era.2021003 |
[18] |
Xiao-Biao Lin, Stephen Schecter. Traveling waves and shock waves. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : i-ii. doi: 10.3934/dcds.2004.10.4i |
[19] |
Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations and Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 |
[20] |
Emile Franc Doungmo Goufo, Abdon Atangana. Dynamics of traveling waves of variable order hyperbolic Liouville equation: Regulation and control. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 645-662. doi: 10.3934/dcdss.2020035 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]