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

TL;DR

This paper establishes explicit convergence rates for the fast-reaction approximation of the triangular Shigesada-Kawasaki-Teramoto system in bounded domains, improving understanding of the system's behavior in various functional spaces.

Contribution

It provides the first explicit convergence rates for the fast-reaction approximation in multiple Sobolev and Lebesgue spaces for the model.

Findings

Explicit convergence rates in L^ ∞L^2 and L^2H^1 spaces.

Convergence with explicit rate in L^ ∞H^l for all l > 0.

Results valid in physical dimension d ≤ 3.

Abstract

We consider the fast-reaction approximation to the triangular Shigesada-Kawasaki-Teramoto model on a bounded domain in the physical dimension $d\le 3$. We provide explicit convergence rates on the whole domain in $\textnormal{L}^\infty\textnormal{L}^2\cap\textnormal{L}^2\textnormal{H}^1$ and in the interior we prove convergence with an explicit rate in any $\textnormal{L}^\infty\textnormal{H}^l$ for all $l > 0$.