We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion chemotaxis systems{ut=∇・(ϕ(u)∇u)+∇・(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),under homogeneous Neumann...We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion chemotaxis systems{ut=∇・(ϕ(u)∇u)+∇・(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),under homogeneous Neumann boundary conditions in a smooth bounded domainΩ⊂R^N(N≥3),where 0<ψ(u)≤K(u+1)^a,K1(s+1)^m≤ϕ(s)≤K2(s+1)^m withα,K,K1,K2>0 and m∈R.It is shown that ifα−m<4/N+2,then for any sufficiently smooth initial data,the classical solutions to the system are uniformly-in-time bounded.This extends the known result for the corresponding model with linear diffusion.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11601140,11401082,11701260)Program funded by Education Department of Liaoning Province(Grant No.LN2019Q15).
文摘We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion chemotaxis systems{ut=∇・(ϕ(u)∇u)+∇・(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),under homogeneous Neumann boundary conditions in a smooth bounded domainΩ⊂R^N(N≥3),where 0<ψ(u)≤K(u+1)^a,K1(s+1)^m≤ϕ(s)≤K2(s+1)^m withα,K,K1,K2>0 and m∈R.It is shown that ifα−m<4/N+2,then for any sufficiently smooth initial data,the classical solutions to the system are uniformly-in-time bounded.This extends the known result for the corresponding model with linear diffusion.
