Global Existence of Solutions of Nonlocal Geirer-Meinhardt Model and Effect of Nonlocal Operator in Pattern Formation

Abstract

We study the global existence of solutions to a class of nonlocal Geirer-Meinhardt system. This is a two component reaction-diffusion model on a bounded domain in ${\mathbb{R}}^n$, $n\ge 1$, with nonlocal diffusion given by a nonlocal convolution operator. We have used semigroup theory and derive estimate to guarantee global existence. Then we build an $L^b$ functional to bound our solution independent of the nonlocal convolution kernel for $2\le b<\infty$. Next, we have used this result to obtain a diffusive limit similar to \cite{laurenccot2023nonlocal} for our model. We also numerically simulate our model to show the formation of patterns by this model and compare the results with the patterns with the traditional local/classical Geirer-Meinhardt model.

After further examination, we identified an issue in the analysis that cannot be resolved within the current framework of the manuscript. To avoid potential confusion for readers, we respectfully request withdrawal of the paper