Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899909 | Journal of Mathematical Analysis and Applications | 2018 | 13 Pages |
Abstract
In this paper we study the global boundedness of solutions to the quasilinear fully parabolic chemotaxis system: ut=ââ
(D(u)âuâS(u)âÏ(v)), vt=Îvâv+u, where bounded domain ΩâRn (nâ¥2) subject to the non-flux boundary conditions, the diffusivity fulfills D(u)=a0(u+1)âα with a0>0 and αâ¥0, while the density-signal governed sensitivity satisfies 0â¤S(u)â¤b0(u+1)β and 0<Ïâ²(v)â¤Ïvk for b0,Ï>0 and β,kâR. It is shown that the solution is globally bounded provided α+β<1 and kâ¤1. This result demonstrates the effect of signal-dependent sensitivity on the blow-up prevention.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mengyao Ding,