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

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

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 -