Global Existence Results for Gierer-Meinhardt Systems on Time Evolving Domains

Global solutions to a Gierer-Meinhardt model of two substances defined by reaction-diffusion equations are shown in this article. By employing Lyapunov functionals and investigating the regularizing properties inherent to parabolic equations, we rigorously establish the existence and asymptotic behavior of solutions under appropriate assumptions. Numerical simulations are used to corroborate the analytical findings. This research differs from previous work because it relies on spatial domains that vary over time, rather than being static. 2020 Mathematics Subject Classification. 35K57, 35B4. Key words and phrases. reaction-diffusion; activator-inhibitor models; existence of solutions; asymptotic stability; evolving domains.