BOUNDARY CONTROL OF THE NUMBER OF INTERFACES FOR THE ONE-DIMENSIONAL ALLEN-CAHN EQUATION.

The identification of optimal structures in reaction-diffusion models is of great importance in numerous physicochemical systems. We propose here a simple method to monitor the number of interphases formed after long simulated times by using a boundary ux condition as a control parameter. We consider as an illustration a 1-D Allen-Cahn equation with Neumann boundary conditions. Numerical examples are provided and perspectives for the application of this approach to electrochemical systems are discussed. [ABSTRACT FROM AUTHOR]