Abstract
Under suitable assumptions the dynamics of a class of chemical reactions with diffusion is governed by a parabolic partial differential equation with a cubic non-linearity and Neumann boundary conditions. Stationary and homogeneous solutions, stationary but non-homogeneous solutions as well as time and space dependent solutions are possible. By tuning the characteristic parameters of the system we can modify the domain of attraction of the system's equilibria and the way they are reached from different initial conditions. We can also explain the processes of nucleation and hysteresis.
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