Abstract
We study entire solutions of a discrete diffusive equation with bistable nonlinearity. It is well known that there are three different wavefronts connecting any two of those three equilibria, say, 0, a, 1. We construct three different types of entire solutions. The first one is a solution which behaves as two opposite wavefronts (connecting 0 and 1) of the same positive speed approaching each other from both sides of the real line. The second one is a solution which behaves as two different wavefronts (connecting a and one of {0, 1}) approaching each other from both sides of the real line and converging to the wavefront connecting 0 and 1. The third one is a solution which behaves as a wavefront connecting a and 0 and a wavefront connecting 0 and 1 approaching each other from both sides of the real line.
| Original language | English |
|---|---|
| Pages (from-to) | 450-458 |
| Number of pages | 9 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 347 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2008 Nov 15 |
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Keywords
- Asymptotic behavior
- Discrete diffusive equation
- Entire solution
- Wavefront
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Entire solutions for a discrete diffusive equation. / Lin, Yung-Jen.
In: Journal of Mathematical Analysis and Applications, Vol. 347, No. 2, 15.11.2008, p. 450-458.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Entire solutions for a discrete diffusive equation
AU - Lin, Yung-Jen
PY - 2008/11/15
Y1 - 2008/11/15
N2 - We study entire solutions of a discrete diffusive equation with bistable nonlinearity. It is well known that there are three different wavefronts connecting any two of those three equilibria, say, 0, a, 1. We construct three different types of entire solutions. The first one is a solution which behaves as two opposite wavefronts (connecting 0 and 1) of the same positive speed approaching each other from both sides of the real line. The second one is a solution which behaves as two different wavefronts (connecting a and one of {0, 1}) approaching each other from both sides of the real line and converging to the wavefront connecting 0 and 1. The third one is a solution which behaves as a wavefront connecting a and 0 and a wavefront connecting 0 and 1 approaching each other from both sides of the real line.
AB - We study entire solutions of a discrete diffusive equation with bistable nonlinearity. It is well known that there are three different wavefronts connecting any two of those three equilibria, say, 0, a, 1. We construct three different types of entire solutions. The first one is a solution which behaves as two opposite wavefronts (connecting 0 and 1) of the same positive speed approaching each other from both sides of the real line. The second one is a solution which behaves as two different wavefronts (connecting a and one of {0, 1}) approaching each other from both sides of the real line and converging to the wavefront connecting 0 and 1. The third one is a solution which behaves as a wavefront connecting a and 0 and a wavefront connecting 0 and 1 approaching each other from both sides of the real line.
KW - Asymptotic behavior
KW - Discrete diffusive equation
KW - Entire solution
KW - Wavefront
UR - http://www.scopus.com/inward/record.url?scp=48849096173&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=48849096173&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2008.03.076
DO - 10.1016/j.jmaa.2008.03.076
M3 - Article
AN - SCOPUS:48849096173
VL - 347
SP - 450
EP - 458
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -