The solutions in provided reaction--diffusion datasets appear to converge to approximately $0.5$ uniformly in space, rather than to $1$ as expected for the Fisher--KPP equation $u_t = \nu u_{xx} + \rho u (1-u).$
For this PDE with $0 < u_0 < 1$ and periodic boundary conditions, the solution should satisfy $u(x,t) \to 1$ as $t \to \infty$ (by the maximum principle and comparison with the logistic ODE).
However, the solutions in the dataset instead approaches a spatially constant state near $0.5$. This behavior is characteristic of the pure diffusion equation, where solutions converge to the spatial mean.
The solutions in provided reaction--diffusion datasets appear to converge to approximately$0.5$ uniformly in space, rather than to $1$ as expected for the Fisher--KPP equation $u_t = \nu u_{xx} + \rho u (1-u).$
For this PDE with$0 < u_0 < 1$ and periodic boundary conditions, the solution should satisfy $u(x,t) \to 1$ as $t \to \infty$ (by the maximum principle and comparison with the logistic ODE).
However, the solutions in the dataset instead approaches a spatially constant state near$0.5$ . This behavior is characteristic of the pure diffusion equation, where solutions converge to the spatial mean.