Abstract
For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 534-543 |
| Number of pages | 10 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 47 |
| Issue number | 3 |
| State | Published - Jun 1987 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER : DEPENDENCE ON CYLINDER WIDTH. / Bell, Jonathan; Cosner, George.
In: SIAM Journal on Applied Mathematics, Vol. 47, No. 3, 06.1987, p. 534-543.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - WAVE-LIKE SOLUTIONS TO REACTION-DIFFUSION EQUATIONS ON A CYLINDER
T2 - DEPENDENCE ON CYLINDER WIDTH.
AU - Bell, Jonathan
AU - Cosner, George
PY - 1987/6
Y1 - 1987/6
N2 - For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.
AB - For a certain class of scalar reaction-diffusion equations, we show that any solution decays if the cylindrical domain's width is too narrow, whereas if it is sufficiently thick, there are solutions which lie and persist between two traveling wave fronts. These ideas are then generalized to a special class of reaction-diffusion systems occurring in the modeling of competing biological species.
UR - http://www.scopus.com/inward/record.url?scp=0023366144&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0023366144&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0023366144
VL - 47
SP - 534
EP - 543
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 3
ER -