Travelling wave dynamics in the nonlocal dispersal Fisher-KPP equation with distributed delay
We investigate the travelling wave dynamics in the nonlocal dispersal Fisher-KPP equation with distributed delay. The introduction of delay causes the equation to lack the comparison principle, thereby significantly increasing the complexity of studying propagation dynamics. In this paper, we prove...
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| Published in | Nonlinearity Vol. 38; no. 7; pp. 75012 - 75043 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IOP Publishing
31.07.2025
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| Online Access | Get full text |
| ISSN | 0951-7715 1361-6544 |
| DOI | 10.1088/1361-6544/addf0a |
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| Abstract | We investigate the travelling wave dynamics in the nonlocal dispersal Fisher-KPP equation with distributed delay. The introduction of delay causes the equation to lack the comparison principle, thereby significantly increasing the complexity of studying propagation dynamics. In this paper, we prove that the delayed equation possesses a minimal wave speed, which is identical to that of the classical nonlocal dispersal Fisher-KPP equation without delay studied in previous works. Specifically, the delayed equation admits a travelling wave connecting the trivial steady state and a positive steady state if and only if the wave speed is greater than or equal to this minimal wave speed. This result highlights a significant observation: the delay does not affect the minimal wave speed of travelling waves, but may alter their shape. Additionally, we demonstrate theoretically that the equation can also admit monotone travelling waves when the mean of the delay kernel is small. The uniqueness of such monotone travelling waves, up to translation, is also confirmed. |
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| AbstractList | We investigate the travelling wave dynamics in the nonlocal dispersal Fisher-KPP equation with distributed delay. The introduction of delay causes the equation to lack the comparison principle, thereby significantly increasing the complexity of studying propagation dynamics. In this paper, we prove that the delayed equation possesses a minimal wave speed, which is identical to that of the classical nonlocal dispersal Fisher-KPP equation without delay studied in previous works. Specifically, the delayed equation admits a travelling wave connecting the trivial steady state and a positive steady state if and only if the wave speed is greater than or equal to this minimal wave speed. This result highlights a significant observation: the delay does not affect the minimal wave speed of travelling waves, but may alter their shape. Additionally, we demonstrate theoretically that the equation can also admit monotone travelling waves when the mean of the delay kernel is small. The uniqueness of such monotone travelling waves, up to translation, is also confirmed. |
| Author | Dong, Luke Xu, Zhaoquan |
| Author_xml | – sequence: 1 givenname: Zhaoquan surname: Xu fullname: Xu, Zhaoquan organization: Jinan University Department of Mathematics, Guangzhou 510632, People’s Republic of China – sequence: 2 givenname: Luke surname: Dong fullname: Dong, Luke organization: Jinan University Department of Mathematics, Guangzhou 510632, People’s Republic of China |
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| Cites_doi | 10.1007/s00332-018-9445-2 10.1016/j.na.2010.09.032 10.1016/j.jde.2014.01.033 10.1016/j.jde.2022.01.047 10.1017/S0308210504000721 10.1016/S0025-5564(03)00041-5 10.1016/j.jde.2010.04.012 10.1016/j.anihpc.2012.07.005 10.1016/j.jde.2012.01.014 10.1016/j.jmaa.2008.05.057 10.1016/j.jde.2010.04.017 10.3934/dcds.2014.34.3511 10.1016/j.crma.2011.03.008 10.3934/dcds.2017042 10.1007/s00332-020-09642-9 10.1088/0951-7715/22/5/011 10.1007/BF02450783 10.3934/dcds.2003.9.925 10.1515/crll.1980.316.54 10.2977/prims/1260476648 10.1016/j.jmaa.2019.02.010 10.1017/S0308210500002523 10.1016/j.crma.2019.04.007 10.1016/j.jde.2010.11.011 10.3934/cpaa.2016.15.1193 10.1016/j.jde.2021.04.033 10.1016/j.jde.2010.01.009 10.1016/j.jde.2014.09.008 10.1016/0362-546X(78)90015-9 10.57262/die/1408366785 10.1088/0951-7715/22/12/002 10.1088/0951-7715/24/11/002 10.1090/proc/14235 10.1017/S0308210500000688 10.1090/S0002-9939-04-07432-5 10.1016/S0895-7177(00)00175-8 10.1007/s00208-011-0722-8 10.1090/tran/6602 10.1023/A:1016690424892 10.1023/A:1021889401235 |
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| Title | Travelling wave dynamics in the nonlocal dispersal Fisher-KPP equation with distributed delay |
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