石田 祥子

We consider a degenerate quasilinear Keller-Segel system of fully-parabolic type involving rotation in the aggregative term, ut = ∇ · (∇um - uS(u, v, x)∇v), (x, t) ∈ Ω × (0, T ), vt = Δv - uv, (x, t) ∈ Ω × (0, T ), ∇v · ν = 0, (∇um - uS(u, v, x)∇v) · ν = 0, x ∈ ∂Ω, t &gt 0 where Ω ⊂ ℝ2 is a bounded convex domain with smooth boundary. Here S(u, v, x) = (si,j)2×2 is a matrix with s i,j ∈ C1([0,∞) × [0,∞) × Ω). Moreover, |S(u, v, x)| &lt S̃(v) for all (u, v, x) ∈ [0,∞) × [0,∞) × Ω with S̃(v) nondecreasing on [0,∞). It is shown that whenever m &gt 1, for any nonnegative initial data, which is sufficiently smooth, the system possesses global and bounded weak solution. © 2014 IOP Publishing Ltd &amp London Mathematical Society.