کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417386 | 1339290 | 2016 | 13 صفحه PDF | دانلود رایگان |
This paper detects the lower bounds of blow-up time of smooth solutions for the chemotaxis model{ut=ÎuâÏââ (u(u+1)mâ1âv),xâB1(0),t>0,vt=Îvâv+u,xâB1(0),t>0, under homogeneous Neumann boundary conditions in a unit ball B1(0)âR3 centered at the origin, with positive constant Ï and parameter mâR. Under the assumption that (u(x,0),v(x,0))=(u0(|x|),v0(|x|))âC0(B¯1(0))ÃW1,â(B1(0)), it is shown that whenever mâ[23,2], the blow-up time of a classical solution to the corresponding initial-boundary problem has an explicit lower bound measured in terms of Ï, â«B1(0)u0p and â«B1(0)|âv0|2q for appropriate p>1 and q>1. Here we underline that the global classical solution exists and is bounded if m<23, which leads to the assumption mâ¥23 for addressing the properties of blow-up solutions. However, the question of lower bounds of blow-up time for the case m>2 remains open due to technical reasons.
Journal: Journal of Mathematical Analysis and Applications - Volume 436, Issue 1, 1 April 2016, Pages 16-28