Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity

Youshan Tao, Michael Winkler

We consider the quasilinear parabolic-parabolic Keller-Segel system $$ u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \qquad x\inΩ, \ t>0, v_t=Δv -v + u, x\inΩ, \ t…