Abstract
This paper deals with the long time behavior in terms of complete spreading for a population model described by a reaction-diffusion equationwith delay, of which the corresponding reaction equation is bistable. When a complete spreading occurs in the corresponding undelayed equation with initial value admitting compact support, it is proved that the invasion can also be successful in the delayed equation if the time delay is small. To spur on a complete spreading, the choice of the initial value would be very technical due to the combination of delay and Allee effects. In addition, we show the possible failure of complete spreading in a quasimonotone delayed equation to illustrate the complexity of the problem.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1059-1072 |
| Number of pages | 14 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 144 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 1 2016 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Persistence and failure of complete spreading in delayed reaction-diffusion equations. / Lin, Guo; Ruan, Shigui.
In: Proceedings of the American Mathematical Society, Vol. 144, No. 3, 01.03.2016, p. 1059-1072.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Persistence and failure of complete spreading in delayed reaction-diffusion equations
AU - Lin, Guo
AU - Ruan, Shigui
PY - 2016/3/1
Y1 - 2016/3/1
N2 - This paper deals with the long time behavior in terms of complete spreading for a population model described by a reaction-diffusion equationwith delay, of which the corresponding reaction equation is bistable. When a complete spreading occurs in the corresponding undelayed equation with initial value admitting compact support, it is proved that the invasion can also be successful in the delayed equation if the time delay is small. To spur on a complete spreading, the choice of the initial value would be very technical due to the combination of delay and Allee effects. In addition, we show the possible failure of complete spreading in a quasimonotone delayed equation to illustrate the complexity of the problem.
AB - This paper deals with the long time behavior in terms of complete spreading for a population model described by a reaction-diffusion equationwith delay, of which the corresponding reaction equation is bistable. When a complete spreading occurs in the corresponding undelayed equation with initial value admitting compact support, it is proved that the invasion can also be successful in the delayed equation if the time delay is small. To spur on a complete spreading, the choice of the initial value would be very technical due to the combination of delay and Allee effects. In addition, we show the possible failure of complete spreading in a quasimonotone delayed equation to illustrate the complexity of the problem.
UR - http://www.scopus.com/inward/record.url?scp=84954510961&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84954510961&partnerID=8YFLogxK
U2 - 10.1090/proc/12811
DO - 10.1090/proc/12811
M3 - Article
AN - SCOPUS:84954510961
VL - 144
SP - 1059
EP - 1072
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 3
ER -