کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6418552 | 1339343 | 2014 | 8 صفحه PDF | دانلود رایگان |
We consider a quasilinear parabolic-parabolic Keller-Segel system involving a source term of logistic type,(0.1){ut=ââ (Ï(u)âu)âââ (Ï(u)âv)+g(u),(x,t)âΩÃ(0,T),vt=Îvâv+u,(x,t)âΩÃ(0,T), with nonnegative initial data under Neumann boundary condition in a smooth bounded domain ΩâRn, n⩾1. Here, Ï and Ï are supposed to be smooth positive functions satisfying c1spâ©½Ï and c1sq⩽Ï(s)⩽c2sq when s⩾s0 with some s0>1, and we assume that g is smooth on [0,â) fulfilling g(0)⩾0 and g(s)⩽asâμs2 for all s>0 with constants a⩾0 and μ>0. Within this framework, it is proved that whenever q<1, for any sufficiently smooth initial data there exists a unique classical solution which is global in time and bounded. Our result is independent of p.
Journal: Journal of Mathematical Analysis and Applications - Volume 412, Issue 1, 1 April 2014, Pages 181-188