Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion

We show the existence of locally bounded global solutions to the chemotaxis system $u_t = \nabla\cdot(D(u)\nabla u) - \nabla\cdot(\frac{u}{v} \nabla v)$ $v_t = Δv - uv$ with homogeneous Neumann boundary conditions and suitably regular positive initial data in smooth bounded domains $Ω\subset \mathbb{R}^N$, $N\geq2$, for $D(u)\geq δu^{m-1}$ with some $δ>0$, provided that $m>1+\frac N4$.

No reviews yet.

No comments yet.