The fast signal diffusion limit in a Keller-Segel system (Q1728019)

The author studies the convergence of solutions of the parabolic-parabolic Keller-Segel chemotaxis model to those of the parabolic-elliptic system in the case of bounded domains \(\Omega\subset \mathbb{R}^n\), \(n\geq 3\). The initial data \((u_0,\nabla v_0)\) are supposed to be small in the space \(L^p(\Omega)\times L^q(\Omega)\) with some \(p>n/2\) and \(q>n\). In the case \(n=2\), an analogous result is obtained if \(\|u_0\|_{L^1(\Omega)}<4\pi\).