کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900214 | 1631557 | 2018 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?
ترجمه فارسی عنوان
چقدر محکم لجستیک می تواند مانع از نفوذ سیستم حداقل سیستم کلر-سگل شود؟
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
We study nonnegative solutions of parabolic-parabolic Keller-Segel minimal-chemotaxis-growth systems with prototype given by{ut=ââ
(d1âuâÏuâv)+κuâμu2,xâΩ,t>0,vt=d2Îvâβv+αu,xâΩ,t>0 in a smooth bounded smooth but not necessarily convex domain ΩâRn (nâ¥3) with nonnegative initial data u0,v0 and homogeneous Neumann boundary data, where d1,d2,α,β,μ>0, Ï,κâR. We provide quantitative and qualitative descriptions of the competition between logistic damping and other ingredients, especially, chemotactic aggregation to guarantee boundedness and convergence. Specifically, we first obtain an explicit formula μ0=μ0(n,d1,d2,α,Ï) for the logistic damping rate μ such that the system has no blow-ups whenever μ>μ0. In particular, for ΩâR3, we get a clean formula for μ0:μ0(3,d1,d2,α,Ï)={34d1αÏ,if d1=d2,Ï>0 and Ω is convex,310â2(1d1+2d2)α|Ï|, otherwise. This offers a quantized effect of the logistic source on the prevention of blow-ups. Our result extends the fundamental boundedness principle by Winkler [42] with d1=1,d2=α=β:=1/Ï, Ω being convex and sufficiently large values of μ beyond a certain number not explicitly known (except the simple case Ï=1 and Ï>0) and quantizes the qualitative result of Yang et al. [52]. Besides, in non-convex domains, since μ0(3,1,1,1,Ï)=(7.743416â¯)Ï, the recent boundedness result, μ>20Ï, of Mu and Lin [25] is greatly improved. Then we derive another explicit formula:μ1=μ1(d1,d2,α,β,κ,Ï)=α|Ï|4κ+d1d2β for the logistic damping rate so that convergence of bounded solutions is ensured and the respective convergence rates are explicitly calculated out whenever μ>μ1. Recent convergence results of He and Zheng [9] are therefore complemented and refined.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 459, Issue 2, 15 March 2018, Pages 1172-1200
Journal: Journal of Mathematical Analysis and Applications - Volume 459, Issue 2, 15 March 2018, Pages 1172-1200
نویسندگان
Tian Xiang,