Improved convergence rates in the fast-reaction approximation of the triangular Shigesada-Kawasaki-Teramoto system

Abstract

We consider the fast-reaction approximation to the triangular Shigesada-Kawasaki-Teramoto model on a bounded domain in the physical dimension d ≤ 3. We provide explicit convergence rates on the whole domain in 𝐿 ∞ ⁢ 𝐿 2 ∩ 𝐿 2 ⁢ 𝐻 1 and in the interior we prove convergence with an explicit rate in any 𝐿 ∞ ⁢ 𝐻 𝑙 for all l > 0.