Growing domains

We consider the Gray-Scott system on uniformly growing domains. For an overview of some of the dynamics in such systems, and an introduction to the literature, see this SIAM dynamical systems gallery.

• Check out this interactive simulation on a linearly growing domain. By default, the simulation shows a kymograph or space-time plot of the solution $u$ in time and space. You can press to change instead to a 1D plot of the density of $u$ as a function of $x$.

• There is also an interactive simulation on an exponentially growing domain. These simulations are made using a field $m$ to store the 1D solution in snapshots of $y$, so that the $y$ axis in the kymograph represents the time coordinate. Playing with the domain indicator function, as well as the Overlay submenu under allows you to design your own kymographs for growing or static domains.

Check out this 2D growing simulation for a crude implementation of the Schnakenberg system on a growing domain with Dirichlet boundary conditions.

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