Global Existence Of Solutions For A Class Of Chemotaxis Model

In this dissertation,we consider the following parabolic-parabolic-parabolic Chemotaxis Model:(?)in a bounded domain Ω(?)Rn,n≥1,with smooth boundary.Under the assumptions that with some K1,K2>0,β-≥β+,we have K1e-β-s≤D(s)≤K2e-β+s for all s≥0,and that the size of S relative to D and R relative to D can be estimated according to S(s)/D(s)≤K3eγs and R(s)/D(s)≤K4eαs with some K3,K4>0 and γ,α∈[(β+-β-)/2,β+/2),we obtain the global existence of classical solutions for all reasonably regular initial data,as well as a logarithmic upper estimate for the possible growth of ‖(·,t)‖L∞(Ω)as t→∞ with f(u,v)=-v+u,g(u,w)=-uw or g(u,w)=-u+w.