Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension
We deal with the boundedness of solutions to a class of fully parabolic quasilinear
repulsion chemotaxis systems
{
ut = ? · (?(u)?u) + ? · (ψ(u)?v), (x, t) ∈ ? × (0, T),
vt = ?v ? v + u, (x, t) ∈ ? × (0, T),
under homogeneous Neumann boundary conditions in a smooth bounded domain ? ? R
N (N ≥3), where 0 < ψ(u) ≤ K(u + 1)α, K1(s + 1)m ≤ ?(s) ≤ K2(s + 1)m with α, K, K1, K2 > 0 and
m ∈ R. It is shown that if α ? m < 4N+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.
关键词：
chemotaxis,
repulsion,
quasilinear,
fully parabolic,
boundedness,
high dimension
