Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222262 | Nonlinear Analysis: Real World Applications | 2017 | 16 Pages |
Abstract
In this paper we study the chemotaxis-system {ut=ÎuâÏââ
(uâv)+g(u)xâΩ,t>0,vt=Îvâv+uxâΩ,t>0, defined in a convex smooth and bounded domain Ω of R3, with Ï>0 and endowed with homogeneous Neumann boundary conditions. The source g behaves similarly to the logistic function and verifies g(s)â¤aâbsα, for sâ¥0, with aâ¥0, b>0 and α>1. In line with Viglialoro (2016), where for αâ(53,2) the global existence of very weak solutions (u,v) to the system is shown for any nonnegative initial data (u0,v0)âC0(ΩÌ)ÃC2(ΩÌ) and under zero-flux boundary condition on v0, we prove that no chemotactic collapse for these solutions may present over time. More precisely, we establish that if the ratio ab does not exceed a certain value and for 95
Related Topics
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Engineering
Engineering (General)
Authors
G. Viglialoro,