Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222063 | Nonlinear Analysis: Real World Applications | 2018 | 27 Pages |
Abstract
In an earlier work (Rachidi et al., 2017) by the authors of the current paper, traveling wave solutions of the above chemotaxis system with Ï=0 are studied. It is shown in Rachidi et al. (2017) that for every 0<Ïcâ(Ï) and ξâSNâ1, the system has a traveling wave solution (u(x,t),v(x,t))=(U(xâ
ξâct;Ï),V(xâ
ξâct;Ï)) with speed c connecting the constant solutions (ab,ab) and (0,0). Moreover, limÏâ0+câ(Ï)=2aif01.We prove in the current paper that for every Ï>0, there is0<ÏÏâcâ(Ï,Ï)â¥2a satisfying that for every câ(câ(Ï,Ï),cââ(Ï,Ï)) and ξâSNâ1, the system has a traveling wave solution (u(x,t),v(x,t))=(U(xâ
ξâct;Ï),V(xâ
ξâct;Ï)) with speed c connecting the constant solutions (ab,ab) and (0,0), and it does not have such traveling wave solutions of speed less than 2a. Moreover, limÏâ0+cââ(Ï,Ï)=â,limÏâ0+câ(Ï,Ï)=2aif0
Related Topics
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Engineering (General)
Authors
Rachidi B. Salako, Wenxian Shen,