TY - JOUR
T1 - Entire solutions for a discrete diffusive equation
AU - Guo, Yung Jen Lin
N1 - Funding Information:
This work was partially supported by the National Science Council of the Republic of China under the grant NSC 94-2115-M-003-009. E-mail address: [email protected].
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
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U2 - 10.1016/j.jmaa.2008.03.076
DO - 10.1016/j.jmaa.2008.03.076
M3 - Article
AN - SCOPUS:48849096173
SN - 0022-247X
VL - 347
SP - 450
EP - 458
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -